the.com/last resort

means The only remaining option left after every preferable one has failed or been used up.

from 'Resort' comes from Old French resortir, 'to resort, rebound, or return to,' itself from Latin sortiri, 'to draw lots, obtain by chance' (the same root that gives us 'sort'). A 'resort' was originally a place or recourse you turn to — the thing you fall back on. 'Last resort' simply marks the end of that line: the final recourse left once every earlier, better one has run out.