Is there a bound on possible Dead state in a minimized DFA
If you allow the DFA to be trimmed, then you can delete ALL dead states. If you want the DFA to be complete, then the minimized DFA will indeed have at most one dead state.
The reason is that minimizing leads you to merge nondistinguishable states, that is equivalent states in the Myhill-Nerode equivalence relation (here the definition is given for words and languages, but it can be extended to automata).
Two states $q_1, q_2$ are distinguishable if there exists a word $u$ such that $\delta^*(q_1, u)$ is final and $\delta^*(q_2, u)$ is not (or the converse). If $q_1, q_2$ are two dead states, then $\delta^*(q_1, u)$ can never be final (and same for $q_2$), so $q_1, q_2$ will never be distinguishable.