If your felloship is over, but your Ph.D. is not, you can ask for unemployment benefit in Belgium. Your are not required to be Belgian for this. It is enough that you worked XXX days in the last years in Belgium. Another important requirement is that you payed the relative taxes within your fellowship, and this is usually the case. Probably you did not notice it because it was done directly by ULB.
There are several entities involved in the dole. The first, and probably the most important for you is the ONEM. They are the ones who actually have the money. You will seldom deal with them though.