If you can show that you are in danger of persecution you can try to apply. If you missed the one year filing deadline you may still be eligible for withholding of removal if you can show it is more likely than not that you will be persecuted in Haiti.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
A lot depends on a number of facts you did not disclose. You should talk to an immigration attorney in person.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.
TPS for Haitians was extended in March of this year. If you re-applied by 5/2/2014, you are eligible for an EAD (work permit). Depending on your age and other factors, you may also be eligible for Deferred Action for Childhood Arrivals. An asylum claim at this late date is probably not going to be approved unless you have a credible fear of prosecution and changed or extraordinary circumstances. If it is denied by USCIS, you will be put into removal proceedings. You have a complex case and should consult with an experienced immigration attorney to find out which options may be available to you.
The opinions expressed by Joanne Tinsley, Esq. are made based on a general understanding of the topic at hand and without the benefit of knowing all of the pertinent facts of your case. Her answers do not establish an attorney/client relationship.