That's a tough question. It's like asking, "What happens to people when they get on a subway train?"
Any number of things can happen depending on what the individual's purpose or Intent was in getting on the train in the first place.
The thing about people who commit suicide is that the usually do it from a place of emotional desparation, grief, anger, loss, or other similar energetic state.
This low-energy state continues after the spirit separates from the body and makes it more difficult for that spirit to recognize its new relationship to The Universe and continue into the next experience. Until they can resolve the issues which led them to end their lives, they can not make the transition. They are like a record with a scratch: they just keep focusing on the problems and can never seem to let go of the pain or negativity that brought them to that state.
It has been my experience that there are a number of "helpers" (Guides, Allies, Ancestors, Angels...call them what you will) who help these spirits regain their perspective. Certain individuals who are still in this experience may also interact with these spirits to assist them. The living who act in this capacity are known as "Psychopomps" and they work with spirits in order to help them continue their journey.
I have done this 32 times. Over 1/2 (17 to be precise) of the spirits I have worked with were suicides. Of those 17, I was able to help none to continue on directly. It is my hope that the work I did with them made it possible for them to be helped further by others.