It’s common for people to be partly at fault for injuries that happen on someone else’s property. For example, if you are walking on someone else’s property and trip because you didn’t see a crack in the sidewalk.
In terms of whether you’d be able to sue in such a circumstance, it really depends on how much of the blame can be put on you and on the property owner. There are also various laws that pertain to partial liability that differ between states. It’s advisable to speak with an experienced premises liability lawyer to find out whether or not your case has any validity.