Your SSDI benefit will remain exactly the same no matter where you move to. Even if you were getting SSI, in addition to SSDI, that would also remain the same, regardless of where you moved to.

If you were getting SSI, then any additional state benefit would vary, depending what state you moved to.

I'm wondering if it might be possible for someone who doesn't get SSI to get a state supplemental benefit. I would think that might be possible if your SSDI were an amount that caused you to just barely miss being eligible for SSI (in addition to your SSDI.) Notify SSA of your move. Then I would advise you to see about applying for New York's state supplement, if your SSDI benefit is under $808.

Check these links:

If I am moving to another state, do I need to re-apply for disability benefits?

https://www.health.ny.gov/publicatio...ity_income.htm

If you have a Section 8 voucher that subsidizes your housing rent payment, that can change, depending where you live.