"become subsumed" is correct and usable in written English.
You can use it when talking about an entity (person, thing, or idea) being absorbed or encompassed by a larger entity. For example, "The small local business eventually became subsumed by a giant corporate conglomerate."
They have become subsumed into his world.
Those around at the time (eg, Aliweb, JumpStation and WebCrawler) have long since been pensioned off, or become subsumed in some other service.
As Daniel Barenboim demonstrated with his East West Divan Orchestra, when people of differing views are brought together in a collaborative and creative endeavour, differences become subsumed.
However, the government must ensure that our aid programme does not become subsumed in our military or security objectives and that DfID's poverty-reduction mandate is resolutely defended.
"I just see it as the thing that replaces all the things you normally carry around: cellphones, pagers, wristwatches, all those things become subsumed into one item," he said.
He excels at combining sweetness with wackiness so that even if he's playing a man dealing with a collapsing house (The Money Pit), a smart aleck policeman (Dragnet) or a man in love with a fish (Splash), the part doesn't become subsumed in either slush or silliness.
Laurie Garvey drifts somewhat aimlessly into this cult and then becomes subsumed by it.
Their work became subsumed into that now unfashionable genre known as "Commonwealth writing".
A true analysis becomes subsumed under the tired old supply-reduction strategy.
"I've always felt that he was a far better character actor than people gave him credit for but he became subsumed within this peculiar persona".
Soon, she finds the work-life balance untenable and becomes subsumed by anxieties about both work and the disintegrating home front.
