That is a tough call to make and a difficult situation to be in. One way to deal with this situation is to be proactive and if possible, take cerain steps to ensure that you have another option available to you before the unemployment benefits run out.
While we may have a sense of security when we are on unemployment, we need to recognize that it is a false sense and even though it may pay some of the bills in the short term, one has to take steps from day one to ensure that there is something else to fall back on; not when the unemployment runs out but before it does. I know this is easier said than done sometimes but the day you start on unemployment you should be looking for work on a daily basis and relentlessly.
It is sometimes difficult for some, not all people, to give up unemployment and take a job instead.
Another thing one can do is to take courses and upgrade your skills while on unemployment so that you are better prepared when it runs out.
If the benefits run out and you are still not employed then you may need to consider getting help to start a small businesslike online jobs, daycare etc. Sometimes we need to try something different.