Will a union-company work for a non-union company?

Will a union-company work for a non-union company?
There are many more details that would have to be provided to be able to answer this correctly. There are severals factors that come into play:

1) What Unions are the company signatory with?
2) What is the size of the Union outfit?
3) What region of the country or world are you in?

Depending on the crafts in which a company is signatory with can determine whether or not they will accept the job. For instance, Joe owns an Electrical Contracting company and he performs no other scopes of work. ABC Non Union General Contractors comes into the area to build a hospital and want to use Joe for all of the electrical components of the scope. Joe can accept this job without violating his contractual agreement with the Electrical Workers. As long as he himself does not employee non-union craftsman of his trade he is not in violation. In fact many of your larger jobs acros the nation are run by Non Union outfits. Most of them are not even craftsman. Most have developed companies comprised solely of managers (i.e.- McKinney & Co.) that all they do is provide Project Management for the venture. They operate very similar to a residential GC in that they do not carry technical units with them. Once they secure a job they bid the scope out in piece mill fashion.

In an opposite direction it is very bad juju for Union Contractor to hire a Non Union subcontractor. There are ways around the sense of being bound to the use of Union Subs but they better make sure they have their ducks in a row because they WILL be visited by the Local Building Trades, seeking an explanation.