A switch controls a plug, not the other way around , as you posted. Electricity is not somehing to deal with on a carefree, 'you know what I mean basis'. You must get it right.
If you were talking about a switched receptacle, one where a wall switch controlled a lamp plugged into it, then it is common practice to wire the recepatacle so only one of the two plug positions—commonly the upper—is switched and the other is always live, as with ordinary receptacles, so either plug could have 'fried' leaving the other working. But it is much more likely that whatever would have done that would have caused the breaker they shared to trip. It is vital to note the two sides may not share the same breaker. You MUST KNOW, before you do anything w/ that receptacle.
The other guys are all onto the other, more likely possibility, that each of the two plugs in the receptacle is being fed by a different circuit, on a different breaker. This is where you MUST GET IT RIGHT. Do nothing with that unit until you KNOW, and KNOW YOU HAVE SHUT OFF ALL power to it. Properly installed split receptacles have the two breaker levers pinned together so that if one trips, the other goes too. But until you know, do not assume your spilt receptacle was properly installed.
If you meant the receptacle also supplies a light switch, I'd ask how do you know? What have you done so far? And I hear Elmer The Safety Elephant saying, "If you're smart enough to ask, you're smart enough to put the plate back and go no further until you post a concise, accurate description of what exists and what you have done. Then wait for the answers."