Let's say that some piece of DNA would be subject to extreme negative selection if it were independently inherited, but it is very closely linked to an extraordinarily fit gene, and so the complex it belongs to is positively selected for.
Is there a term for this phenomenon?
Genetic hitchhiking / genetic draft
From wikipedia
Genetic hitchhiking, also called genetic draft or the hitchhiking effect, is when an allele changes frequency not because it itself is under natural selection, but because it is near another gene on the same chromosome that is undergoing a selective sweep.
The term "selective sweep" is used improperly in the wikipedia definition. One should replace the last sentence by [..] but because it is near another allele on the same chromosome that is undergoing positive selection or if we want to reuse the term "sweep", once could say [..] but because it is near another allele on the same chromosome that is sweeping to high frequency
Selective sweep
From wikipedia
A selective sweep is the reduction or elimination of variation among the nucleotides in neighboring DNA of a mutation as the result of recent and strong positive natural selection.
(For the direct answer to your question skip to the end!)
Genetic linkage can affect the spread of other genes. The degree of linkage, affected by the rate of recombination between the point (nucleotide, gene etc.) directly under selection and the other point. If the rate of recombination between to given points is low then linkage between them is high and occurs either because the region has low rates of recombination (rates of recombination can vary across a genome) and/or because the two points are physically very close. When two loci are associated by linkage such that they are more often associated with one another than would be expected under random conditions, they are said to be in linkage disequilibrium.
Selection on linked loci relates to a number of key terms:
Selective Sweep
When a new beneficial mutation arises (or an existing mutation becomes strongly beneficial) and its frequency in the population rises rapidly because of selection. This causes the loss of genetic variation at that locus, and at linked loci, because variants linked to the beneficial mutation also spread (see genetic hitchhiking below). The hardness of a sweep is the result of the strength of selection; hard sweeps occur when selection is very strongly in favour of the allele.
Genetic Hitchhiking / Genetic Draft
This occurs when the frequency of an allele is affected by selection in other loci. This effect is very apparent in Y chromosomes where most of the chromosome does not recombine with the X. Effectively selection then acts on this single non-recombining unit, such that if a deleterious mutation arises on a Y with many good alleles then it will fare better than a similar mutation that arises on a Y with fewer good alleles. This is one reason that the Y chromosome is low in genetic variation; good variants cannot get away from bad variants at other loci, recombination allows mutations to be reshuffled and therefore raises the likelihood of making very good combinations of alleles.
"Under the classical view, recombination allows deleterious mutations to be eliminated more efficiently, and increases the rate at which favourable alleles can be brought together, despite their association with deleterious alleles." - Barton
The effect (signature) under a selective sweep is to see a decline in genetic/molecular variation around a given point (the point being the variant that was directly under selection), with variation being negatively correlated with the linkage (molecular variation increases with genetic distance from the locus that swept). Hard sweeps then have an obvious signature, but soft sweeps are more difficult to spot; soft sweeps can occur when selection on a novel mutation is relatively weak, or when selection suddenly favoured an existing neutral mutation (which therefore had time to become associated with multiple variants by recombination).
Background Selection
Similarly, if a variant is associated with deleterious alleles then it will come under background selection. In this case, neutral alleles can be removed from a population by the action of selection on deleterious variants at other loci. Again, the strength of selection and degree of linkage disequilibrium will affect the rate at which genetic variation is lost at a given locus.
"Under background selection, neutral alleles that are linked to detrimental alleles are driven to extinction, with more drastic effects when recombination rates are low." - Cutter and Payseur
Hill-Robertson effect
The benefit of recombination should be apparent to you from the above descriptions, linkage disequilibrium will slow the rate of adaptation, and the formal name for this is the Hill-Robertson effect (or Hill-Robertson interference), named after the scientists that described it. If there is no recombination in a species with two genes, each with two alleles then the most fit combination of alleles can only occur if the beneficial mutations occur in the same genetic background; recombination allows beneficial mutations to occur in separate lineages and come together later on. Specifically, if locus 1 has two alleles A and a where A is beneficial, and locus 2 has alleles B and b where B is beneficial, the most fit individuals would have A and B, but without recombination these individuals can only come about if the mutation from b->B (or a->A) occurs in an Ab (aB) individual; recombination allows the AB type to come about even if the A and B have distinct origins.
The phenomenon you describe (deleterious mutation spreads by linkage to beneficial mutation) is a form of interference. Adaptation, which would occur by i) spreading the beneficial allele at one locus and ii) purging the deleterious allele at the other locus, is being impeded because the two are under linkage disequilibrium. The net selection effect for this "complex" is closer to neutral than one (or both) selection effect for either locus. One could describe the phenomenon with something like:
"The deleterious allele spreads, despite its very deleterious effect, by Hill-Robertson interference caused by tight linkage to a highly beneficial allele."
Note (and credit to @DermotHarnett): Haplotype is the proper word for what you called a "complex".
