What is て form at the end of sentences when it is not a request


I understand that the phrase ごめん、待たせてしまって! means "I am sorry (and regret) that
I made you wait". This statement does not look like a request. Why is a て form
and not past form た used here?




This seems to be simply a colloquial rearranging of the usual "grammatical"
order

> 待たせてしまってごめん（ね・なさい）

(see [How do you say thank you for or sorry
for?](https://japanese.stackexchange.com/q/12529/1628))

This happens all the time. Parts of the sentence are left out and put in after
the more relevant parts have been said. For illustrative purposes one might
take a very simple sentence りんご（を）食べたよ and rearrange it to 食べたよ、りんご.

> りんご食べたよ  
>  食べたよ、りんご




This seems to be simply a colloquial rearranging of the usual "grammatical"
order

> 待たせてしまってごめん（ね・なさい）

(see [How do you say thank you for or sorry
for?](https://japanese.stackexchange.com/q/12529/1628))

This happens all the time. Parts of the sentence are left out and put in after
the more relevant parts have been said. For illustrative purposes one might
take a very simple sentence りんご（を）食べたよ and rearrange it to 食べたよ、りんご.

> りんご食べたよ  
>  食べたよ、りんご

