Annual reports are obligatory in Estonia

Yes, even if you do not have any business, the annual reports are mandatory. There is no way to "suspend" your company other than to liquidate.

The county court has been very active recently regarding companies not submitting their annual reports. First they will give a deadline of usually 30 days and afterwards they will issue a fine. The fine can be many thousands of euros and can be issued both to the company and the responsible persons meaning the board members.

It is true that if the person getting the fine lives in another country then actually getting the payment of the fine can be challenging. But there will consequences meaning that you could not get your e-residency renewed and also if you wish to apply for a visa or residence permit in the future then it can be seriously impacted.

If you have no economic activity then submitting the annual report (has to be done before the end of June following the reported year) is not so difficult. There are resources available that teach this and even using an accountant for it will not be too expensive. If you have stopped the activities all together then the proper way to go about is to close your company for good - it can save you from problems in the future.