Nothing. This is the single most common way open-source work misleads people, and it misleads them in the direction of confidence.
A search that returns no results tells you that the sources you asked did not answer with a match. It does not tell you the record does not exist. Consider what has to be true for an absence to mean anything:
- every source that could hold the record was asked;
- each one was working at that moment;
- the name was spelled as that source spells it;
- the source publishes the kind of record you are looking for at all.
Any one of those failing produces an empty page that looks exactly like a clean record. Most registers are national, most are incomplete, and transliteration alone — Sergei, Sergey, Serhii, Serhiy — will hide a person from three sources out of four.
So write it the way it is true. "No match was found in the sources listed below, on this date" is a finding. "This person has no record" is a claim you cannot support, and the difference is one somebody may rely on.