Juri Linkov <juri@linkov.net> writes:

[ Sorry i forgot to reply. ]

>> The patch is not yet finished, this feature is currently "hardcoded"
>> (the only way to disable this is removing `tab-line-tab-face-modified`
>> from `tab-line-tab-face-functions`).
>>
>> I would like any suggestion, if should this have an option for disable
>> this.

> There is an option `tab-line-tab-name-format-function`,
> but it would be too cumbersome for users to override the
> whole `tab-line-tab-name-format-default` to be able to
> disable only the close button.

Indeed.  I've added an option for allow disable this.

> Maybe it would be ok for users to customize the icon with
>
>   M-x customize-icon RET tab-line-close-modified RET
>
> and copy attributes from `tab-line-close-button`.

AFAIK the icon should be customizable.

I'm sending here the finished version of the patch: