You seem to be misunderstanding what vertical and horizontal modes are.
First of all, let me consider the relationship between vertical and horizontal mode. TeX always starts off in vertical mode.
Under certain circumstances (precisely when it sees a horizontal command), TeX leaves vertical mode and starts horizontal mode in order to make paragraphs. You can't “leave” this mode in other ways than ending the paragraph.
You're probably misled by the name of the \leavevmode command, which could have been named something like \StartMakingAParagraphIfItMakesSense; the command does \unhbox\v@idbox and \unhbox is a horizontal command, so
- (unrestricted) horizontal mode is started if TeX was in vertical mode,
- nothing happens if TeX is in horizontal mode or in math mode.
The only way to end unrestricted horizontal mode is by issuing (explicitly or implicitly) a primitive \par command. Every vertical command, if found when TeX is in unrestricted horizontal mode, issues a \par token.
Note that \par might not mean the primitive \par, but the redefined \par should at some point execute the primitive \par or strange things will happen: the simple
\def\par{}
x\vskip1pt
will start an infinite loop, for example, because \vskip will continue to issue \par in order to be executed in the vertical mode that's never reached.
You can start vertical mode when in horizontal mode by opening a \vbox or \vtop, but the resulting list will eventually be appended to the horizontal list being built, so this doesn't seem what you're looking for.
There is an escape to the surrounding vertical mode: if TeX finds \vadjust{...} in (unrestricted) horizontal mode, it will package the vertical list given as argument, and this list will be inserted between the line where the command happens to be and the next one, after the paragraph has been formed. Such a vertical list will be appended before the interline glue. So
abc\vadjust{\vskip3pt} text text ... text
will have 3pt of additional vertical space between the first and second lines of the paragraph.
There is no symmetry between vertical mode and horizontal mode, because they do very different things.
\par. What you're asking in the final paragraph doesn't make sense: in horizontal mode you make paragraphs. – egreg Mar 30 '15 at 08:49\parinsert a new line/line break as well? – sdaau Mar 30 '15 at 08:51