If you can work out a mutually acceptable arrangement with the landlord, that's great. If not... The sublessor is a landlord, and is subject to all of the security deposit laws of your state. If the sublessor does not comply with the law, you can sue in small claims court.

If you fail to pay your rent the sublessor can initiate the eviction process, but... I'm not seeing that they'll find it worth the expense and bother, particularly given that it's unlikely that they could get an eviction order before their lease term ends. That said, if your not paying your rent means that the sublessor doesn't pay her rent, that could create issues with her landlord. I'm not sure what, if anything, you've signed with the sublessor's landlord (other than your lease starting April 1).