As others have stated, he can file a lien against your property. However filing of the lien requires certain deadlines be met, notice requirements be satisfied, and it also requires that he bring legal action to "perfect the lien" within 360 days (assuming no technical defaults). You have rights to shorten that period. You may want to discuss this matter with a knowledgeable attorney to determine if you need to act at this time and to review your specific circumstances.
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While the lien can be filed, liens law are very technical and even the slightest mistake and void a lien. In addition, you can force the lien claimant to sue the first plumber within 60 days by filing and service a notice of contest and if no suit is filed, along with a Notice of Commencement of Lien Action (which is another very technical document) you can get the lien thrown out. Many attorneys mess up liens so it is possible this plumber did too. If he did not mess, your course of action should consider the amount of the lien and the costs and time involved in dealing with this. If is a small amount, do you want to hire an attorney or go to court, or try and settle. At the end of the day the lien claimant will only have a claim on your property and would have to wait for you to sell or refinance - its not a personal judgment - using this as a negotiating ploy may entice him to take the money and run, so to speak.
This is not intended to create an attorney client relationship and none is to be implied either. You must contact an attorney and present all facts before you can and should act on this response
Others have correctly stated that the plumber who did the work can file a lien. The question is, what do you do next? As one answer notes, you can file a notice of contest of lien that forces the worker plumber to sue your regular plumber within 60 days. That may force payment to the claimant. Other answers have noted there may be mistakes that would void the lien, but those require your proving defects in the lien filing or notice process, and take up your time. The first question for you is: Does the lien cause you any problems, such as a lender requiring you get it off the title? If so, and depending on the size of the lien, you may want to pay the plumber in exchange for a lien cancellation and get him to assign his claim to you. Then, with the plumber who regularly does work for you, you have the leverage of the assigned claim and the enticement of future work. It seems to me the regular plumber would value the working relationship with you and get you paid off in cash or trade. I'd be happy to discuss this further with you if you like. Good luck!