Yes, but only in that large groups are unbalanced; intentionally taking risks to deal finishing blows is uncommon
The D&D 5e Dungeon Master's Guide (p.82) does indeed note that encounters with large groups are significantly more deadly, in part for their ability to swarm a single target:
The more monsters there are, the more attack rolls you're making against the characters in a given round, and the more dangerous the encounter becomes.
However, enemies intentionally prioritizing unconscious PCs is quite uncommon, as most creatures simply don't benefit from intentionally killing downed PCs while there are still living people to fight.
This tendency for DMs to avoid killing PCs unnecessarily is typical of modern editions of D&D; early editions lacked a death save mechanic entirely, and it was more common for DMs to be adversarial. Matt Colville says, in his video Trust and Earth Elementals:
I think I assumed, like most people do, that the bad guys will stop focusing on someone once they go unconscious, and go after the immediate threat, the conscious players.
Why might a monster choose not to execute fallen foes right away?
Many enemies are unintelligent and fight instinctively, without any regard for tactics. If that's the case, then a monster who mortally wounds one player character will want to quickly shift focus to the other player characters who pose a more immediate threat.
Many enemies fight tactically or with some purpose. Again, the smart option is usually to ignore the wounded PC and focus on his allies, who pose an immediate threat. Finishing off unconscious PCs when there are still enemies alive is like looting the battlefield before the fight is over.
Of enemies sufficiently smart, brave and dedicated enough to kill a PC when the fight is still ongoing, few have the necessary intent. You'd need to be willing to risk your life, and the lives of your allies, just the make sure that one guy dies right away when he's already unconscious and bleeding on the floor, and about twelve seconds away from death anyway.
Even so, there may be value in capturing PCs alive if possible, such as to ransom, sell into slavery or interrogate for information. The enemies may be subject to laws or a moral code which prevent them from executing prisoners.
Even if the attackers have the specific goal to assassinate a certain party member, they may readily mistake an unconscious and dying PC for a dead one, especially in the chaos of battle.
Importantly, however, the DM may simply not wish to kill your beloved character. This is a critical factor which has certainly saved many thousands of characters. Even the death save mechanic itself exists to give downed PCs a fighting chance.
However, your fallen PCs are not necessarily safe!
As other users have noted, there are some circumstances where an enemy will really want a target dead dead, particularly if the DM wills it. Intelligent opponents who see an unconscious party member restored to the fight with healing magic may suddenly lose faith in the wisdom of ignoring unconscious NPCs.
Matt Colville famously tells a story:
"Wait, wait, Matt, hang on. I'm unconscious. You're going to attack somebody else, right?"
"Oh no. The earth elemental steps on your head, to make sure you're dead."