Liable state
The liable state is the state legally responsible for paying an unemployment claim — the one where the claimant's base-period wages were reported. Moving to another state never changes the liable state: the claim, weekly amount, and duration all stay with it, and the claimant files as an interstate claimant.
This is why "transferring" an unemployment claim is impossible and unnecessary. The destination state has none of your wage records and cannot pay you; the old state can and must, wherever you live.
Interstate claimants usually must register for work with the new state's workforce agency and follow the liable state's work-search rules from their new address.
Federal source: US DOL — Unemployment Insurance ↗
Related terms: Combined Wage Claim (CWC) · Base period