A dirty, shirtless homeless man sits on the sidewalk, holding his cup up to passerby asking for change.
A homeless man begs.
If the homeless man is holding his cup up to passersby that indicates he is begging, and thus can simply be rephrased as A homeless man begs.
The homeless man holding his cup and asking for change is the same as saying he begs.
Asking for change can be considered begging.