How should events without a year be indexed?

LegacyUser

Paul said: The current problem is that any record that is indexed with only a day and month (because the actual year is missing / unclear in original entry) is treated as if it took place during this century. The example below shows how a birth, that obviously took place in or before 1781 (probably 19 April 1781), is found in a search for a William Miller born in 2019.

Is there any way around this problem - either in the indexing process or when the source is added to FamilySearch?