Imagine that I live and work in Massachusetts. I am being laid off by the end of the year. I already have a new job but it won't start until a few months after the end of my current employment. I know that collecting unemployment benefits requires me to be "able, available, and actively seeking work" (see here). Does this mean that I am no longer eligible for unemployment insurance benefits?
Actively looking for work (3 work search attempts made on 3 separate days)
New Jersey, where I twice applied for and received unemployment benefits, has an almost exactly similar rule. I can tell you that in NJ, an applicant must be able to provide the names and addresses or telephone numbers (or other contact info, such as email addresses) of at least three potential employers who s/he approached in some way each and every week that s/he claim benefits, even after the applicant had already has a contingent offer of employment with a start date. If the applicant does not certify three attempts to look for work on the weekly application, no benefits are authorized that week. If the applicant does certify but cannot provide the names on request, that is considered a false application, and incurs a penalty, over and above denial of benefits.
An "approach" can include sending out a resume, answering an ad, going to a job fair, or telephoning a possible employer, or other methods of contact. It is a good idea to maintain a log of all your contacts, because if the state decides to review your case (which they can do for any of several reasons) they may ask you to provide your contacts for any or all of the weeks you claimed benefits.
Generally, most unemployment benefits programs require you to be actively seeking work. If you aren't planning on continuing your job search, then no, you would not be eligible. For MA it appears to be a two step process, applying for unemployment benefits and then requesting weekly payments. While you may be eligible to apply, you would then fail the weekly request because you did not seek employment. See the state's relevant website here.