Is it legal for a previous employer to have a law firm demand a settlement you did not agree upon?

It really depends on the circumstances underlying the demand, but in general, you are not bound to terms of an agreement you did not make or as to which you did not accept benefits. However, if (for example) you accepted severance benefits notwithstanding that you did not actually sign a proposed severance or release agreement, there may be an argument from your former employee that by accepting the benefits of the agreement, you tacitly agreed to the terms accompanying your acceptance of those benefits. Again, your individual circumstances will dictate your obligations in the matter. You would be well served to contact an attorney to consult with you about the communication from your former employer and about your duties, obligations, or potential liability- if any- particularly, if you are receiving communications and demand for performance from their attorneys.

If the settlement was not signed/agreed upon, the lawyer will not prevail.