I hired a full time person with equity-only compensation. The higher-than-usual rate reflects that. However the contract was not professionally written as it only mentions the equity part. Can that person still claim a salary?
Hard to comment reliably without seeing actual wording, but if there is a question now, I would recommend getting professional advice, i.e., lawyer specializing in employment issues. Yes, having an employee and not paying them is a problem, but if the person has an equity position in the company, there may be a case for them being "just" one of the owners and not subject to employment laws per se. Again, hard to know without seeing the contract wording, but if things seem vague to you now, get professional advice sooner rather than later - it's cheaper in the long run by several orders of magnitude!