The landlord is not free of liability risks. In California, everybody is responsible
for injury brought about by lack of ordinary care or skill in management of his or her property or person. This applies to landlords, falling under Business Proprietor’s Liability for the Criminal Conduct of Others.
Therefore the landlord must use
reasonable care to protect tenants and guests from another
person's harmful conduct on the property if the conduct can be can reasonably anticipated. The duty is towards anyone on tenants and guests alike. To figure out whether the landlord has breached his duty of care, the courts will "balance" the probability of harm to the tenant with the burden of the duty imposed on the landlord to prevent or mitigate the risk of harm, see Vasquez v. Residential Investments, Inc., 118 Cal. App. 4th 269. In that instance, the landlord failed to replace a missing pane of glass on the front door, contributing to the tenant's murder, for which the landlord was held liable (wrongful death). This ruling has extensive discussion of that balancing act. The crucial question is, how did the assault happen, and how do the landlords actions relate to the assault?
The answer may be different in other jurisdictions.
In the modified scenario, liability would hinge on scenario details (I'll continue to assume California). The factual question is whether in light of the background check, the assault was foreseeable, and to what extent it was preventable – what did the landlord do wrong? For instance, if the criminal history check revealed a number of arrests for assault in the state and the check was limited to CA (the new tenant moved to CA just a year ago), and if the assault was in old-tenant's room which had no lock due to landlord indifference, then the landlord is more likely to be held liable (he could have fixed the lock for a few dollars, or paid for a better criminal check). On the other hand, if a thorough criminal check reveals no arrests or complaints for anything, anywhere, and the assault happened in the common area while talking politics, there is no reasonable course of action that the landlord could have undertaken to prevent the assault (hiring 24 hour guards would not be reasonable, in this scenario). In Vasquez, the issue came down to the landlord's failure to implement a cheap fix on the front door.
In a third version of your scenario, suppose that there was some evidence of past violent behavior, but the only fault that could be assigned to the landlord is the fact of renting to the new tenant. Does a landlord have a duty to deny housing to a person with a past record of violent behavior?
It is legal in California to do background checks and deny a prospective tenant a lease based on existing criminal history, as long as the criteria are applied consistently (not discriminatorily), and not in a jurisdiction where criminal checks are illegal (Oakland).
There is a non-fantasy scenario where that includes "the US", given a guidance from HUD, based on a disparate impact analysis. HUD says that a housing provider excluding applicants with arrest but no conviction
"cannot satisfy its burden of showing that such policy or practice is necessary to achieve a substantial, legitimate, nondiscriminatory interest". If there are convictions and there is a blanket no-convict policy, the provider
must still be able to prove that such policy or practice is necessary
to achieve a substantial, legitimate, nondiscriminatory interest. A
housing provider that imposes a blanket prohibition on any personw ith
any conviction record –no matter when the conviction occurred, what
the underlying conduct entailed, or what the convicted person has done
since then – will be unable to meet this burden
If it is illegal to discriminate on the basis of past convictions, a landlord cannot be held liable for obeying the law. In short, "it depends (on minute details and whether the plaintiff's lawyer makes the necessary arguments): ask your attorney".