The death saving throw is, as both the name implies and explicitly defined in the rules, a saving throw. It also has the particular rule...
Rolling 1 or 20. When you make a death saving throw and roll a 1 on the d20, it counts as two failures. If you roll a 20 on the d20, you regain 1 hit point.
But notably... that does not say the 1 or 20 automatically succeed or fail, the way it does for attack rolls and critical hits. So let's consider...
Roll a d20. If the roll is 10 or higher, you succeed
But looking at these two, there can be a strange interaction - what happens if I have a total bonus to all saving throws of +9 or more, and I roll a 1?
And before somebody says a +9 is unreasonable, consider a mixture of the following:
- A nearby Paladin's Aura of Protection.
- The bless spell.
- An Artificer using flash of genius to advise me how not to die.
- Being a monk with the Diamond Soul feature which gives proficiency in all saving throws.
- Magic items such as the cloak of protection or ring of protection or stone of good luck.
- A Peace Domain Cleric's Emboldening Bond.