If your relative disappears, one possible reason for the disappearance is a change of name. Sometimes these name changes will appear in local court records. In the early days of a state or territory, these changes may have been recorded at the state level. Ancestors who immigrated may have changed their name when they naturalized. Others may never have legally changed their name even if they did in practice.
Land records may mention multiple spellings of a name, particularly if a deed of purchase has a different spelling than a deed of sale. Probate records may mention alternate names for a person if receipts and documents have names that don’t match. Pension records may also document a name change.
And…if the person changed their name because they were running from the law, there may be no record.