Yes, and there is legal precedent for inmates winning significant awards in exactly this kind of situation.
The Eighth Amendment to the Constitution prohibits cruel and unusual punishment, and courts have consistently held that prison officials have a legal duty to protect inmates from known dangers. When staff are made aware of a threat or an actual attack and deliberately do nothing, that indifference can rise to the level of a constitutional violation. Cases where guards have been proven to act as lookouts while an attack took place have resulted in successful lawsuits against correctional facilities and individual officers.
That said, winning such a case requires evidence, and building that evidence starts immediately after the incident.
The first step is filing a formal grievance through the facility's administrative process. This creates an official record that the incident was reported and that a response, or lack of one, was documented. Every grievance should be copied to someone on the outside who can preserve that paper trail. If the grievance process gets ignored or produces no result, that itself becomes part of the record.
Any injury from a stabbing must be reported to medical staff immediately, both for treatment and because the medical report becomes critical evidence. Photographs of injuries, written accounts of what happened and what was said to guards, and names of any witnesses all strengthen a potential case.
An attorney who handles prisoner civil rights cases is the right person to evaluate whether a lawsuit is viable. Many take these cases on contingency, meaning no upfront cost. The grievance record you build inside is what gives them something to work with.