As an introduction, you really need to read Sanhedrin 78a-b with Rashi, and Rambam Hilchos Rotzeach Ushemiras Nefesh 4, which lay out the practically applicable rules of assessments, which will answer any specific question. The only possible question arises if an original assessment was made that it had the power to kill, and we do not accept any subsequent assessments that the person should no longer die as a result.
However, locally in this Passuk, the answer is given by Shadal to Shemos 21:19, that if he gets better, and dies later, we assume that it was due to not taking enough care of it:
על משענתו – על מקלו, מיד ינקה המכה, אף אם אח״כ ימות המוכה, כי יש לתלות שהוא גרם לעצמו שלא נשמר כשהתחיל להבריא
This sounds like if there is 100% evidence that it was directly caused, the person would be chayav. See the commentary of RDZ Hoffman (link above), who understands this discussion not to be a "ta'ama dekra" situation, but rather, a relevant halachic question.
Before I looked it up, I wrote the following cute pilpul shel hevel:
While I don't have a source that directly addresses the issue, I do have an interesting Mar'eh Makom (or Moreh Makom - I'll ask that as a question soon) that talks about a somewhat related case.
A Petzuah Daka(h) or Kerus Shafchah are men who sustain injuries to external genitalia, which the Torah forbids to "marry into the congregation" of Israel (Devarim 23:2, Alhatorah translation):
לֹֽא־יָבֹ֧א פְצֽוּעַ־דַּכָּ֛א/דַּכָּ֛ה וּכְר֥וּת שׇׁפְכָ֖ה בִּקְהַ֥ל י״י׃
He who is wounded in the stones, or has his privy member cut off, shall not enter into the assembly of Hashem.
The Talmud (Yevamos 75b, translation based on Davidson Edition) qualifies this statement by noting that if it was "in God's hands", it does not disqualify this individual :
אמר רב יהודה אמר שמואל פצוע דכא בידי שמים כשר אמר רבא היינו דקרינן פצוע ולא קרינן הפצוע
Rav Yehuda said that Shmuel said: A man wounded with crushed testicles at the hand of Heaven, is fit to marry a woman who was born Jewish.
While the meaning of "at the hand of Heaven" is a dispute among the Rishonim, a question could arise similar to what was asked by the OP - what if man-made trauma caused a later illness to develop (according to some, illness is considered "the hand of Heaven"), which eventually rendered the man a Petzuah Dakah. The Chazon Ish (Nashim 10, my rough translation) says:
ועוד יש לצרף דאפשר דאין כאן פסול בידי אדם דתחלת ההכאה לא עשתה פסול אלא גרמה מיחוש קצת, ומה שנעשה לאחר חמש שנים מקרי "ע"י חולי"
...And it is should also be combined that it is possible that there is no disqualification through "the hands of man", because the original trauma did not cause a disqualification, rather, it caused a small injury, and what happened 5 years later would be called "through illness".
He rules that when there was a significant gap (and recovery), the later damage may not be associated with the original injury. However, he says that this is "possible", and may only be using it here since ruling this way will result in the person being permitted to marry into the congregation, so I wouldn't read into it too much.