A proper morphism is defined as separated, of finite type and universally closed. I wonder if the requirement of being of finite type is superfluous, i.e. if being not of finite type implies not universally closed. Recall that a morphism is of finite type if and only if it is locally of finite type and quasi-compact.

In an answer to this question Bjorn Poonen showed that not quasi-compact implies not universally closed.

Is it true that being not locally of finite type (plus possibly quasi-compact) implies not universally closed?