Yes it does vary state to state even though it is a Federal program. I think it is called WIA funding (workforce investment act). Many states and counties (CA,NC,WI,FL...) have an "Employment Training", or "One-Stop" employment center, or "Workforce Development" section that is separate from the unemployment department, with lots of phone numbers. Tell them your company has downsized, the jobs were sent overseas, and you need extra training to find a job. Each state/county seems to have a distinctly different approved list of training providers. I found the amounts they will give you vary from $500.00 (WI) to $3500.00 (CA) which might help you pay for part of a type rating. Also, contact the training providers directly and they can send you helpful info.
Best of Luck.