When things droop from heat, lack of water, or illness, they wilt. If you go on vacation for two weeks and forget to water your plants first, they will wilt.
The vegetables in your garden will wilt if they're attacked by slugs or don't get enough moisture — and people can be said to wilt too, especially when they're limp and weak from exhaustion. A long walk on the hottest day of summer can make you wilt. Wilt was most likely first spelled welk, from the Middle Dutch word welken, "to wither or become soft."