It depends on the kind of suit. If it is the defense of a suit filed against you, or another kind of suit where there is little to no chance of recovering fees, the attorneys will most likely stop their representation of you.
If there is a chance for recovery of fees against the opposing party, the attorneys might be willing to continue, but probably not. If that had been the situation the attorneys would have taken the case on a contingent fee basis in the first place. The attorneys might be willing to work out a payment plan, so that is something you can discuss with them.
But in the end, what it comes down to, is that the attorneys will not continue their representation of you if there is little chance that they will ever be paid for their continuing efforts.
If you cannot pay, your lawyers will notify the judge of your inability to pay and seek permission to withdraw, which will, barring extraordinary exceptions (not generally applicable in a civil case), be granted. You can then seek to continue on your own or perhaps try to settle the case if that is a possibility for you.