[verb て-form] + 済む + 話/こと/問題 (modifying a noun)
The grammar pattern て済む (てすむ) expresses that a situation can be resolved, settled, or gotten through by doing the action described. It conveys the idea that the action in question is sufficient to handle a problem or that things turn out okay with just that much effort or consequence.
When attached to the て-form of a verb, 済む indicates that doing that action is enough to resolve the matter.
The negative form て済まない (or て済まされない) emphasizes that a certain action is not enough to resolve the situation – the problem is too serious.
Combined with the negative て-form (ないで), this pattern means to manage without having to do something – often implying relief that the undesirable action was avoided.
When used with a noun + で, the pattern means that just that amount or thing is sufficient.
This pattern often carries a nuance of relief or surprise that the outcome was better (lighter, cheaper, easier) than expected.