I would run my beta_lockinfo to see what is going on. This will answer which of the two options that applies:
- The process is blocked.
- The process is running a slow query.
In the latter case, beta_lockinfo will give you the query plan of the current statement. If you are on SQL 2019 this plan will have the actual values so far - great to find misestimations. You can also get this on SQL 2016/2017, but this requires that TF7412 is in force.
Would the process be running a loop, another tool on my web site can help you to get more information. With sp_sqltrace you can snoop the spid for some time (default ten seconds) and sp_sqltrace will aggregate recurring statements so that you get totals.
Not surprisingly, both these tools requires permission. For beta_lockinfo, you need VIEW SERVER STATE and for sp_sqltrace you need ALTER TRACE. If you don't have these permissions, you need to pester your DBA to run them for you. If you pester her/him often enough, you may eventually get these permissions.
On the other hand, if you don't have these permissions, you can claim that it is not your job to deal with these situations.