he is not talking about going outside of the country. he is asking abt whether he should apply for TPS or not whose deadline is dec 24 of 2015.
here is my reasoning :

scenario no 1, when he doesn't apply for TPS.
- if his case is approved, its all good.
- if his case is denied, he goes to immigration court. different courts on that matter.....many years...then if its approved, its still good. if not, he will be on deportation.
- or the immigration judge can deny his case, deny him to send to the court and put on deportation right away.

scenario no 2, when he applies for TPS. extra $500 (plus $700, $1300 extra in total) if you hire a lawyer
- if your asylum is approved, you lose $500 (or $1300).
-if your asylum is denied, you can either choose to go to court or abandon the asylum case (provided your TPS is approved, which will if you dont have any criminal case) and still be be on TPS.
- you will never be in fear of deportation.
even if it is called TPS and valid till dec 2016, it will definitely be renewed for a couple of times. so atleast it will be valid for 5-7 years. only thing is TPS will not lead to any other statuses while asylum will give you a GC if it gets approved. having said that you can apply for both TPS and asylum at the same time. if you applied for asylum before your visa expired or became out of status (sevis terminated), when you apply for TPS and get approved, you might still be in legal status (you have to check with a lawyer for sure) and can file for GC through employment later.
so apply for TPS without EAD (provided you have EAD through asylum). it will be like a backup and safety blanket. its only matter of $1300.
bro, don't think, just do it. msg me if you have any questions.