Currently the counter integrations does not allow negative values for its init value. It will result in an validation error ( see https://github.com/home-assistant/core/issues/74076 )
This is an artifical limitation which doesn’t make sense. You can set negative values for min and the counter will happily decrement below 0 if this is allowed.
→ please remove the positive int limitation for initial counter values, so that positive and negative values are allowed for this field.
For my usecase: I “calculate” elevation of a solar panel, which might be a positve or negative number, with initially having a negative angle.