Substitute the best available records: the employment contract, pay stubs or tax slips, work samples with dates, and a declaration from a former supervisor, together with a short explanation of why the letter could not be obtained.
Reconstruct the period with independent records
Officers accept that companies close, managers move on and some employers decline to write letters. What they will not accept is an unexplained gap in the three years. For a missing period, assemble the signed employment agreement showing the start date, the record of employment or the final pay stub showing the end date, tax slips for the years in between, and published or internal documentation samples that bear her name and a date.
A declaration from a former supervisor or colleague, giving their contact details and describing her duties, adds the narrative the letter would have supplied. Put a one-paragraph cover note in the file stating which employer is covered this way and why. Keep the substitute evidence to the specific period and do not let it replace letters that are obtainable from other employers.
Hypothetical example: a technical publications writer can obtain only a short letter from a former software firm because its records were archived after a merger. She should first ask for a letter that gives dates and technical-writing duties, then use payroll records and dated manuals or API references only to fill the stated gap. The officer needs a coherent period-by-period record, not a pile of duplicate papers.
An unexplained change of title or employer is a reason to add a concise chronology before travel.