The Falling Devil in Chainsaw Man proved to be an intriguing presence since she was first introduced. A Devil whose mere arrival on Earth caused shockwaves and led to a number of Humans taking their own lives. She was powerful enough to even compel Yoru to retreat. However, as seen early on, the Falling Devil looks to be subservient to other Devils, the Death Devil in particular.
She was last seen in the Falling Devil Arc before making another appearance very recently alongside Lady Death. But what stood out in her latest surfacing was her behavior. Although the series positions her as dutiful to others, her relationship with Death could be different. This is not related to the Death Devil's ability to control her targets post-consuming them, i.e., something more unique.
Disclaimer: This article is a speculative theory and reflects the writer's opinion.
Chainsaw Man's Falling Devil may share a distinctive bond with the Death Devil

The events of Chainsaw Man chapter 198 and 199 seem to showcase a unique relationship between the Falling Devil and Lady Death. Although known to act on the directions of other Devils or "for Hell as a whole", the latter was oddly attentive to the Death Devil. This can be first traced back to the Falling Devil's debut in chapter 122.
She immediately ceased attacking Denji and Asa Mitaka upon the arrival of "Fami" and apologized for her failure. Now back to the present, she acts according to the Death Devil's directions and restrains the real Famine Devil and Fakesaw Man for Death to consume. She even looks out for her, urging her to cover herself and later even praising her for her power.
Nonetheless, the idea that Falling is serving the Death Devil of her own free will seems have become popular in the fandom. It is plausible, given that falling, both physically and mentally, does tie into death. There is also a possibility that what Yoru said (high-ranking Devils revere Death) is true. So, the Falling Devil obeys Death out of veneration and since Death is likely the most powerful.
Death likely made Falling a pawn long ago

While the idea that Chainsaw Man's Falling Devil obeys Lady Death of reverence is compelling, previous events suggest otherwise. Referring back to the Falling Devil Arc, she halted her attack once the Death Devil appeared. While apologetic for her failure, Death orders her to "return" which transforms her into a miniature figurine similar to the real Fami and Fakesaw Man.
This all but confirms that the Falling Devil has always been one of Death's tools. But it is unclear when this happened. Now given that both Devils are Primal Fears and have been around for quite a while, Death may have realized Falling's importance. Since their powers are most likely linked, having this sort of Devil as a minion would eventually prove to be very handy.
Thus, she may have leveraged the Falling Devil's subservient nature to somehow consume and gain control of her. Once that was done, Death's powers increased manyfold, having such a powerful ally to call upon when necessary and completely obedient.
In Conclusion

The Falling Devil and her loyalty to Death in Chainsaw Man is definitely an intriguing point of discussion. But the events at the end of the Falling Devil Arc all but cement that the Death Devil controls her through and through. However, there is cause for debate, given that Falling herself questions (chapter 199) Death regarding the need to "consume" to exert control.
The Death Devil doesn't answer her directly, only stating that "meat tastes best fresh" and "savoring lives as much as possible is good manners". So, until further revelation, it wouldn't be incorrect to assume that Death's ability to control beings may work in different ways, consumption being one. Thus, with Falling and now Fami and Fakesaw Man as pawns, Lady Death has something terrifying in store.
Related links:
- Chainsaw Man: How the Falling Devil represents Asa's ultimate challenge, explained
- Pochita's true identity in Chainsaw Man is related to birth (but not how fans think)
- Chainsaw Man chapter 201 release details