So basically, you have three different types of 'things' (for lack of a better term): You have that which is necessary, that which is contingent (you have a choice), and that which is necessary but only because it must be so after a contingent choice has been made. So it's necessary, but not to begin with, and is necessary in a very different way. I guess you could call that which was necessary to begin with, necessarily necessary, and that which is necessary by choice, not necessarily necessary. But of course, am sure there's a better word, or at least term, to describe this phenomenon.
One of the senses of entailment applies:
- something involved as a necessary part or consequence of something:
Long hours of work are an entailment of the job.
That (originally unnecessary) thing has now become necessary because it is incidental to the other activity (choice that you made).
2 (incidental to) Happening as a result of (an activity):
‘the ordinary risks incidental to a fireman's job’
‘For instance, a charity has to refrain from political advocacy, unless such lobbying activity is merely incidental to the charitable purpose.’
If thing A is not an inherent requirement for an overall process P, but is a requirement if you choose to implement thing B, then A is a requisite for B.
A requisite is something required to achieve a desired goal or comply with something else. For example, if you work at Joe's pizza emporium, you can make pies, but if you want to deliver the pizzas, you need a driver's license. Having a valid driver's license is a direct requisite for being a Joe's delivery driver. Furthermore, having a valid license requires having a certain level of car insurance, so having that insurance is an indirect requisite for delivering Joe's pizzas.
A possible future condition, indirect effect or result of something (e.g. a choice) is an implication.
Definition: something implied; a close connection.
Example: The newspapers discussed the implications of the president's election.
How about logical necessity or modus ponens?
logical necessity: that state of things that obliges something to be as it is because no alternative is logically possible; a thing that logically must be so
modus ponens: the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the antecedent (p) holds, then the consequent (q) may be inferred
In the context of your question, all this means is that if A is a choice, and if A being chosen implies that B is necessarily true, then the consequence B is a necessary result of the choice A.
Depending on your specific meaning, here's two phrases that may or may not apply:
"Mission creep" -- a military term referring to the inevitable broadening of the scope of the initial mission once boots are on the ground.
"Inheritable error" -- you want to go to the store to buy milk, but you can't find your key, then you realize your husband accidentally took your keys with him that morning so you go to call him, but your phone is out of battery, so you go to charge it, but you find your dog has chewed on your charger and destroyed it, and in doing so broke a tooth, so now you have to, by necessity, a) go to the vet, b) buy a new cell phone charger, c) charge your phone, d) divorce your husband... e) and you still haven't gotten any milk.
Your description the mechanism by which the the thing becomes necessary is very vague. However if the choice that led to the thing becoming necessary was the very choice to actually use the thing in the first place, the term addictive comes to mind.