A person or business is not financially responsible for an injury (liable) simply because the injury occured on his or its property; rather there must be fault, or something they did wrong, for liability to attach. In a case like this, if there were some potholes or other dangerous spots/areas in the parking lot, which your partner tripped in, the center may be liable since it may be negligent, or careless, to not fix such conditions in a medical/rehab center parking lot. But if there were no unreasonably dangerous condition, it is most likely that they are not liable, since they would have done nothing wrong.