Republicans do that?
Not in public they don't outside of some blue states. I've never heard a Republican admit some people need welfare.
I've noticed Republicans will insist on absolutes a lot. For instance if one person is cheating, they'll demand the program be ended or refuse to donate money to a good cause. In contrast, most Democrats seem to accept that a certain percentage of any social welfare program, public or private, will go to the undeserving poor. That is just the cost of operating any such program.
I've yet to figure out if this is based in the Conservative religions, which also seem to insist on a sharp line between the elect and the sinners or if it is based in their political ideologies, which seem to always assume that you should make a hard rule "three strikes and you're out" or "zero tolerance" and then follow that to the inevitable absurd conclusion, a top down declaration, rather than a bottom up "hey what works to fix the problem?" that leftists seem to favor.