From the very specific way you phrased that? Maybe. The injury could become infected, but the whole thing about it being on the ground is kind of a red herring. That is to say, it doesn’t really matter.
Any knife that hasn’t been fully, carefully, cleaned, can be a potential vector for infection. Post injury, clothing, ambient debris, and even improperly sterilized bandages can result in infections.
There’s actually a small irony in that infections for gunshot wounds come from the stuff being forced into the wound after the injury, not from the bullet itself.
Dropping the knife on the ground, getting dirt or grass smeared on it could result in the blade carrying more bacteria, but, unless it was sterilized before the fight, that would already be the case. I’m not sure how the odds work out on it picking up bacteria, but, it kind of doesn’t matter.
Outside of some specific situations, backtracking and figuring out exactly where an infection came from is wasted energy.
So, you have a character that’s stabbed. The wound could become infected. Without access to proper medical care that could kill them. It doesn’t really mater if the knife has been dropped or not. It doesn’t matter if the bacteria came from the knife, or the victim’s shirt, or their own hand, when they grab the wound because, “surprise, you just got stabbed.”
The one time you do need to track down the source of an infection is when it’s a persistent, recurring issue. Cases where you have a colony of legionnaires’ disease or staph in a hospital, for instance. You see patients getting sick from it regularly, but the vector ends up being in the hospital itself. Another example would be commercial food contamination, such as an E. coli outbreak. But, when it’s a single infection, tracking the vector isn’t usually a priority.