At some point in the fight, when it is opportune, you send in reinforcements, equal in number to the wasted minions. The new minions will require new actions to kill, thus preserving the assumed economy with respect to minions and encounter design.
You could be adding a ton of XP to the encounter, or making the players wonder why they're getting "ripped off." Also many/most fights are short so the bosses could easily be killed before your second wave could plausibly get there "hey why didn't we see them coming!" making the extra minions just easily killed sacks of XP.
I could see doing something like this occasionally, like for the final boss fight of an adventure or if you want to feed the PCs XP because they're falling behind for some reason, but I wouldn't use it as a general solution.