Check your opponent's escape routes for a weak group very carefully before moving in for the kill.
That is, don't play nakade moves, in particular, against a group that may still escape or connect out. That doesn't mean that one shouldn't remove the base; that's a typical way of chasing a group while making profit.
If you do concentrate on destroying eye shape as well as eye space, before closing off all escape routes, then
A situation where this proverb might be applied is when the territories are already defined, and collapsing a group's eye space forces it to flee into territory you more or less control. A vicious tooth-and-nail fight inside what was your own territory is not something you want unless you know you can win.
(I think invented this one. -- BlueWyvern)
Edited - Charles Matthews