It stops a surcharge, it does not delete the claim
Forgiveness means your current carrier will not raise your premium for a first at-fault accident. The accident still happened, it still appears in your claims record, and another carrier quoting you later will see it and rate for it. The benefit is real and it is narrower than the name suggests.
It usually has to be earned
Most programs require a period of claim-free driving before the benefit applies, or charge for it outright. Buying a policy today rarely means being forgiven tomorrow, which is worth knowing before relying on it.
It generally does not transfer
Forgiveness is a feature of that carrier’s rating, so switching companies usually leaves it behind. That is one of the quiet costs of shopping, and it is worth weighing against the saving rather than ignoring either.