I have come across quite a number of issues where customers state that when they do a search in WebUI they are able to see inactive transactions. Take a look at the screenshots below, transaction “Opportunity Default” is INACTIVE
The behaviour under search functionality is correct. All transaction types (including inactive) should be displayed in the search. The reason behind it is that when transaction type (OPPT) was active, users might have created documents of that type. Later when that transaction (OPPT) is changed to inactive, the search should still be able to display the documents pertaining to erst while active transaction type (OPPT). Therefore the visibility of the inactive transaction types is appropriate. The create button DDLBs however would not display the inactive transactions to avoid further creation.
Test it yourself.
But if you implement Note 1461152 (manual corrections required as well), then you can stop inactive transactions from being displayed.