When a personal injury lawyer states that they have a no-win no-fee policy, that typically means that if the firm takes your case and does not win a verdict or settlement, there will be no fee due.
The real question is: are such firms right for your case?
Many states specifically limit the amount a personal injury lawyer can charge for a case and that limit is usually defined as a percentage of the total amount won, sometimes adjusted on a declining sliding scale as the award amount increases. Personal injury law firms that have a no win, no fee policy usually accept plaintiff cases, but typically do not work gratis on defendant cases.
The no win no fee lawyer bases the decision on whether or not to take a case on a number of factors: injury, liability and coverage and takes a risk with every case, in that there is no way to guarantee a verdict or settlement will be won.
Having your plaintiff case accepted by a personal injury lawyer on a contingency basis is a very good sign that a verdict or settlement might be won, and having it rejected by three or more law firms probably means there is very little chance of winning the case.