In order to avoid this you just don't let people pay less than a minimum survivable hourly wage so they can't force the government to subsidize them.
In the absence of a minimum wage constraint, and all other things being equal, a change in government assistance is going to result in an opposite change in the market wage rate. This is just a statement of market mechanisms. When the labor pool has access to higher benefits, it is easier for an employer to find someone willing to work for a little less than before (and vice versa).
The two situations are somewhat different though. In the first case you are talking about an individual moving themselves into a different market (unskilled/untrained labor to improved skills/experience, for example). Ensuring that this progression isn't penalized via overly aggressive reduction in benefits is a good thing irrespective of any minimum wage constraints. In the second case you are talking about a global change to the market constraints for all participants.
So I was just responding to the parent to say that when the government changes its "formula" for benefits, it is entirely reasonable and expected for the market to find a new equilibrium. This isn't an example of Walmart or any other employer "using federal money to subsidize their workforce". This is just the market doing what it does.
As for your minimum wage concerns, a minimum wage prices some people out of the labor market entirely. Someone with minimal skills or experience won't be able to bring enough value to an employer to cover the minimum wage. I think it would be much better to get rid of minimum wage rules and adjust benefits accordingly. It makes more sense for someone with minimal skills to have a job (and thus a path towards more skills) and some additional public assistance than to have no job at all and be 100% dependent on public assistance.
In a fictional world without minimum wage or assistance a low wage employee can't afford to work for less than would be required to live for very long so one would expect the wage to float to somewhere in that neighborhood. Lets completely arbitrarily set that value at $10 an hour without worrying what the actual value would be. Imagine that the company expects to create $15 of value on average for each $10 paid out.
Note that in this universe even without a minimum wage the wage still can't float arbitrarily low because people can't live and certain people who truly don't create the needed value are STILL pushed out of the labor market by more employable people. Without any benefits they just die.
Now lets add welfare! People with enough to eat, free medical, cheap rent can indeed afford to work for less even if the company is still generating the same $15 net on each labor hour. Say the person effectively gets $7 an hour in benefits and companies average out to pay $5.
This means that in the original arrangement customers paid out $15 and the employee collected $10 the employer $5.
In the new situation the customer paid out $15, society kicked in $7, and the employee collected $12, the employer collected $10.
One could have achieved the same societal benefit by giving the employees $2.
Nations that provide sizable benefits to poor are obliged to set a minimum wage to avoid the situation where the social safety net represents a net transfer of wealth to low end employers by allowing employees to offer below living wages.
I'm not claiming I have a good solution, just pointing out the side effects of the high minimum wage (higher that the otherwise natural market clearing price).
