Since there is no legal regulation and obligation yet, companies issuing stable coins publish these statements at their own discretion and timeframe.
Audits are a central issue when it comes to stablecoins, as they are coins backed by something. So the question is, whether the purported backing asset is actually backing the coin.
An audit should be conducted by a third party, an independent party.
I can only talk, as an example, about the only stablecoin I'm familiar with:
"On 22nd October 2020 independent officers from Inspectorate International entered the Kinesis vaulting facilities and physically tallied the quantity of gold and silver. Shortly thereafter, the inspectors checked the total against the quantity reported by ABX in the inventory report on 16th October 2020.
As well as recording the quantity, the auditors assessed the quality and weight of a random selection of gold and silver bars. For this purpose, the inspectors carried out tests to assess the weight and fineness of the bullion. Additionally, the auditors assessed whether or not the quality of the storage facility was satisfactory."
https://kinesis.money/resources/kinesis_audit_11-03-2020.pdfI'm sure there are other stablecoins that offer independent audits.
Anyway, without such audits, to be conducted on a regular basis, it's impossible for a stablecoin to take off, to get broad adoption, particularly by institutional actors.