New York follows pure comparative fault (CPLR §1411): your recovery is reduced by your share of the blame but never eliminated. A driver found 40% at fault still recovers 60% of their damages. Adjusters use this aggressively — the recorded statement they ask for in the first week is largely a hunt for admissions that raise your percentage. You are under no obligation to give one to the other driver's carrier, and you should not before speaking with counsel.
The other lever is coverage. New York's minimum bodily-injury liability limit is $25,000 per person — often far below the value of a real injury. We look for every layer above it: the driver's umbrella policy, an employer's policy if the driver was working, and your own SUM (supplementary uninsured/underinsured motorist) coverage, which many New York drivers carry without knowing it. SUM claims have their own notice requirements, so they need to be opened early, not after the liability policy proves too small.