I see. I'm sorry to hear that. A landlord is not "strictly liable" for the actions of a tenant. Rather, the landlord has to have some sort of culpability in the harm. If some fixture that the landlord was responsible for hurt you, for example, the landlord might be liable. But there has to first be a duty to act on the part of the landlord, a breach of that duty, and foreseeable harm. In other words, the landlord had to have had a duty to act, or a duty not to do something, and breached that duty, AND have reasonably foreseen the harm that occurred as a breach of that duty. The mere fact that the tenant does not have insurance will not make the landlord liable (unless it was the duty of the landlord to make sure that the tenant have insurance). As such, you would not have any case against the landlord. You could still sue the tenant, and any judgment that you obtain would be against the tenant (rather than an insurance policy paying) but you wouldn't have a case against the landlord because the landlord didn't do anything, and there's no strict liability in this situation.
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!