Yes, a group counselor should ask a member of the group to leave if he or she can no longer afford to pay for the sessions, because each person has to pay for it. The counselor has to be paid for their time, and a person should not be allowed to be a freeloader. The group has to think about the good of everyone.
Although any rule should not be absolute, the responsibilities for the members of a group counseling session should be fair and equal. If members must pay and one member is unable to pay then it would not be proper to allow that member to continue. Counseling is critical for many people; but, members must all adhere to certain social and financial obligations.
Perhaps, other measure could be looked into first, such as some kind of aid or assistance, rather than simply asking the person to leave. A compassionate but firm approach to payment should be established. After all, one cannot ask a counselor to begin a process that might potentially lead to most of the group failing to pay.
A group counselor can ask a member of the group to leave if that person cannot afford it. These services aren't free unless people are impoverished and they are subsidized. Group sessions can be helpful, but they aren't a panacea for someone's problems. Sometimes a personal counselor is better for one-on-one sessions.
This is how our current system works. If you have no health insurance and you can't afford to pay out of pocket, then out the door you go. With the system set up like this, then the group counselor has every right to send a patient packing for failing to pay. It doesn't matter what type of health service it is.