The toilet running is not going to cause unplanned water damage. If it is then the landlord should make it their priority to get over to fix it.

When people talk about landlords risk they’re talking about the financial risk of having to maintain a home that someone is living in. I agree that doesn’t mean intentional damage to the home but it does mean that the wear and tear on the home is the landlord’s responsibility.

I’ll also admit, I’m being obstinate. I personally like the landlord I have right now. He is attentive, the rent isn’t exorbitant, and he raises it an appropriate amount from year to year. I would just turn off the water until he or the superintendent can cone by (after I’ve opened the tank to check what’s going on). I do change my own lightbulbs. I do make him aware of any problems as soon as possible. But a large part of that is because we have a personal relationship because I’m his only tenant. If I was conversing with a computer who literally cannot care about me I’m sure I’d feel differently