Quote Quoting adjusterjack
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When OP writes that she didn't insure her car she might mean that she didn't carry coverage for theft and damage to her car but still has the state required liability insurance. Lots of people drop the theft and damage coverage on an older car because it lowers the premium.
What she said was "I didn't have car insurance because it lapsed. I haven't had it in 2 months.". That means that she had absolutely no insurance.
Quote Quoting adjusterjack
2 - It's also possible that the employer has no liability for theft or damage done by a resident or guest of the facility and the insurance rep is offering go-away money without any admission of liability and couching the offer in terms palatable to the OP. The possible purpose is to get a signed release from the OP and avoid a larger claim.
I find that possibility to be extremely unlikely, but she's of course free to investigate it.