Confirmed; see bottom section, below.
However, please refer to Provide a way to retrieve questions and answers that have been deleted -- which is "status-planned".
This is a feature, not a bug. And this kind of feature has been requested many times. So, shush please, don't ruin it for us. ;)
Confirmation info:
You can see this behavior (for now) with this API search: [/2.2/questions?fromdate=1466553600&...][2]
Which still includes the deleted question that the OP references:
{
"tags": [
"java",
"c#",
"quartz-scheduler"
],
"owner": {
"display_name": "Kumar"
},
"question_id": 37987057,
"title": "Need a api or widget like Outlook calendar to create Appoitments"
...
According to:
- [Enable searching with deleted:1 for 10k users][3]
- [10K+ users can [still] search any user's deleted content][4]
This behavior should not be allowed as the API doesn't know that I'm 10K (I'm not authenticated), and I certainly don't own the question.
Also, as a 10K user, I see:
Note: only content you own is returned when searching for deleted content
When using normal site search for deleted content.
[2]: https://api.stackexchange.com/docs/questions#fromdate=2016-06-22&todate=2016-06-24&order=desc&sort=activity&tagged=quartz-scheduler%3Bjava&filter=!)EhwvzgXKKsFs376LZp*)y7pMQF4ZMkg9yqlxI1lLkVzxI8uT&site=stackoverflow&run=true [3]: http://meta.stackexchange.com/questions/145060/enable-searching-with-deleted1-for-10k-users [4]: http://meta.stackexchange.com/questions/271062/10k-users-can-still-search-any-users-deleted-content