I have a home in Mt Laurel NJ that I am renting out. My tenant asked to break their lease 4 months early due to them buying a new home. I told them I would do it if they pay at least 2 of the remaining months to cover me incase the house needs repair and sits for a while. The tenant sent me a law in NJ that states the tenant can break their lease and would only be liable for the days it sits empty and said they would do that instead. My question is, if the tenant just bails, am I only able to hold them liable for the period it’s empty or the term of the lease? If this is the case, why even have a lease expiration date if the tenants can leave whenever they want?

Most leases specify the penalties for breaking a lease, so it is unusual to be negotiating with the tenant over how a lease will end.  You may want to include that language next time.

If you have a resident that skips, you can charge their security deposits for the usual items (damage, back rent, etc) and its pretty easy to use up the entire security deposit.  If you choose to go after them for a money judgement, the amount of rent you can typically seek as damages is exactly what you are facing now.  You can get ask back for all the rent you otherwise would have had while the unit sits vacant.

You were only asking for 2 months rent to protect your downside.  If the unit sits vacant for four months, you could ultimately be better off following the legal limits.   If it rents ASAP, you really have't lost much, so, in the end, this seems a non-issue.

As Greg said. You simply re-list the property. In today’s market there should be zero reason its empty 2 weeks. Maybe 3 if there’s a lot of rehab. The tenants haven’t won, and you haven’t lost under this law. You’re ahead of where you would be without a lease or at lease end. This way you’re getting paid rent while you rehab the property, while you advertise it, while you sort through applicants and while you wait for them to move in. So actually you’re better off than a normal turnover. Plus you get to raise rent today’s higher rental rates in most areas. If you don’t think you can fill it in less than 2 months I would put it up for sale and look for a better market. 

I dont understand how in this case the tenant is better off only paying for the time the house sits empty (unless part of the story is missing).   At any rate, this doesn't sound like a problem tenant and they are being upfront asking to be let out of the lease early.   Why make such an issue out it.   Come to an agreement such as having the tenant help you find another tenant - they help you advertise, spread the word, and show the property, etc. in exchange for breaking the lease.   You are then covered with a new tenant in place and the current tenants are free to go - a win win situation.  Easier than the hassle with time and money wasted on pursuing legal avenues.