Learn German: Die Herrschaft war kurz, weil der Feind den König und dessen Erben vergiftete. - The reign was short because the enemy poisoned the king and his heir.

This is the core of your current lesson! If we used seinen (his), it would naturally refer back to the subject of the clause, der Feind. That would mean the enemy poisoned the king and the enemy's own heir. Using the demonstrative pronoun dessen points specifically to the most recently mentioned person, which is the king.

The English translation says heir in the singular, but Erben looks like a plural. Why is there an -n at the end?

The word Erbe (heir) is a masculine weak noun, meaning it follows the n-declension rules. These nouns add an -n or -en in all cases except the nominative singular. Because the heir is the direct object being poisoned, it is in the accusative case, changing der Erbe to den Erben.

Does dessen change its ending depending on the case or gender of Erben?

No. Unlike normal possessive pronouns like sein or mein, dessen does not take adjective endings. Its form is locked based entirely on the gender and number of the owner (in this case, the masculine singular king). Whether the king had a female heir or plural heirs, the word dessen stays exactly the same.

Why is the verb vergiftete placed at the very end of the sentence?