To state the title question perhaps more precisely:
What is the largest photon energy $E_{\gamma}$ and the corresponding mass number $A$ and atomic number $Z$ of a suitable nucleus ${}^A_ZX$ (presumably in a ground state) such that the hypothetical reaction
$$ {}^A_ZX + \gamma \rightarrow {}^{(A - a)}_{(Z - z)}Y + \text{whatever remains (with combined charge} +z \text{)}$$
is "kinematically" forbidden for any values $1 \le a < A$ and $Z \ge z \ge Z + a - A$,
while conforming to the standard model?
Edit
Changed the question title (removed the parenthetical qualification "whether otherwise stable or not"): for any unstable nucleus the stated question and condition is not meaningful and not relevant.
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