Can having broken ribs lead to respiratory failure from asthma?

No: Having broken ribs you may breath shallow, as you are gurading from pain. However, if the ribs are broken, then the ribs can cause the lung to collapse leading to respiratory failure.

No it can not: Asthma can if not treated lead to respiratory failure but broken ribs by itself can not make your asthma worse and cause respiratory failure, unless it causes a pnumothorax which is very rare with rib fractures so answer is it will not except in these cases only theoretically possible.

Indirectly...: Fractured rib can lead to shallow breathing due to pain which can lead to retained secretions. The retained secretions can lead to bronchitis or pneumonia. The bronchitis or pneumonia can lead to an asthma exacerbation that can result in respiratory failure. This would be a relatively rare but theoretically possible sequence of events prevented by deep breathing and secretion clearance.

No: If your asthma is well controlled and you take your meds regularly. The problem occurs if the rib fx on top of an asthmatic attack prevents you from getting enough air. That is, the fx ribs already compromises your breathing and ability to breathe-add asthma to this and you can develop resp failure. Best to get pain relief for the fx.