Why is only she listed on the document? Does it refer to any supplemental document is there any other supplemental document with a list of tenants on?
From what you have said, this seems extremely risky and I would want the tenants listed either on the tenancy agreement there, on the tenancy agreement I would want it to refer to another schedule with the names of the tenants on.
Unless there is something in writing, signed by all the tenants, then an unnamed party is not liable for any commitment with regard to property and that would leave your daughter liable for all the rent if the others defaulted. She would be able to pursue the others but the landlord would not.
Even if they are all named, each of them are jointly and severally liable for all the rental in any event.
Can I clarify anything for you?
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Don’t assume anything. If they all have agreements, then each of the agreements should refer to the other three agreements. I would want to see those agreements. However…
I don’t like four separate agreements for the same property.
There is absolutely no reason why 4 tenants should not be named on this one agreement or if this not room, the agreement annotated and referring to a separate piece of paper.
Based upon this one piece of paper, the only person that is liable is your daughter.
If the other tenants are quite happy with it and they confirmed that they will be responsible for the rent, they will have no problem putting their name on the agreement. As it is, the only person the landlord can chase is your daughter.