"175,000 failed asylum seekers are still awaiting deportation" Daily Mirror
"Officials cannot find 50,000 rejected asylum seekers" The Guardian
"Officials have lost track of 50,000 illegal immigrants and failed to kick out another 175,000" Daily Mail
The Home Office has lost track of 50,000 people, but they are not all failed asylum seekers as stated in the coverage of a report by the Public Accounts Committee reviewing the border and immigration system.
The headline figures refer to cases in the Migration Refusal Pool— those are people who have had an application to stay in the UK turned down, but the Home Office can't confirm if they have since left the country or been allowed to stay as the result of a different application.
They are not all "rejected asylum seekers" as described in the Guardian as it counts all those bids to remain including work, spousal or student applications. The Mirror says that '175,000 failed asylum seekers are still awaiting deportation' but some will have already left and others will have been given permission to stay.
The Mail said that officials had "lost track of 50,000 people and failed to remove another 175,000", but these two numbers can't be usefully added together. The missing 50,000 all come from the pool of 175,000 and were identified by Capita when they were asked by the Home Office to check over Migration Refusal Pool case records in 2012 and 2013.