That'd be essentially a group legal insurance plan - something many employers offer anyway - and you don't really need a union to join one (or offer one, if you wanted to).
I very much doubt companies are going to pay for your lawyers to sue them with.
Legal plan is usually provided by the third party and paid by the employee. The company essentially just rents out the placement in their HR system - but the same plan may be also available independently, there's nothing forcing it to go through the HR specifically.