Can Morbid be triggered after the Morbid creature is cast?
No, but not for the reason corsiKa states. The reason that you cannot do this is because the Ulvenwald Bear's triggered ability has an "intervening if clause." For triggered abilities with intervening if clauses, the condition is checked both when the triggered ability would be put on the stack and once again when it resolves.


  603.4. A triggered ability may read “When/Whenever/At [trigger event], if [condition], [effect].” When the trigger event occurs, the ability checks whether the stated condition is true. The ability triggers only if it is; otherwise it does nothing. If the ability triggers, it checks the stated condition again as it resolves. If the condition isn’t true at that time, the ability is removed from the stack and does nothing. Note that this mirrors the check for legal targets. This rule is referred to as the “intervening ‘if’ clause” rule. (The word “if” has only its normal English meaning anywhere else in the text of a card; this rule only applies to an “if” that immediately follows a trigger condition.)