Debt collectors are precluded under FDCPA 805(b) and 804 from communicating with any third party except to attempt to obtain location information regarding a consumer, and in any such communication with a third party, they cannot disclose that the consumer owes or is aleged to owe any debt. Spouses are considered to be the consumer, and thus are not third parties.
All enacted back in the day before voice mail was prevalent. The FDCPA does not address the specific issue of whether leaving a voice mail, which might be heard by others, is a violation of disclosue to a third party that the person is alleged to owe a debt.
There has been litigation addressing that issue, but the results are apparently not consistent, and until heard at the appellate level, do not become binding case law even within the jurisdiction of a lower court. Maybe someone on the site has recent experience that can be shared, as it is kinda fluent now.
You can file a complaint with the FTC, who may shed some light on their current interpretation of the statute.
You can also research the relevant case law in your jurisdiction, and see if anything has reached the appellate level.
Or your state may be a bit more progressive than the federal FDCPA, and have enacted specific legislation on this issue.