How does OPTION (FAST 1) actually interact with a client?
If it were a query that returned more than 1 row I'd speculate that someone at the vendor (way back when, given the version of SQL Server) stumbled on the query optimiser producing a preferable plan when FAST was specified as a hint. 

As it's returning just 1 row, the explanation probably has more in common with the infinite monkey theorem than reasoned judgement. A junior saw a hint for FAST and decided that was preferable to his query not being fast.


  This makes me wonder if the client has somehow broken communication,
  would the server keep the transaction open, processing the full result
  set after the first n rows are returned and leave the transaction
  open?


The query returns 1 row so there is no further result set to process. I'm inclined to suspect there is other code further up the stack that's causing the problem.