Investigations into nine republicans who were part of a fugitive comfort letters scheme have been completed with no opportunities for progress.
On The Runs (OTRs) were those suspected but not convicted of paramilitary offences, including IRA suspects fleeing potential imprisonment for murders and other serious crimes during the Northern Ireland conflict.
The contentious peace process scheme, agreed between Sinn Féin and the last Labour government, saw letters sent to some republicans informing them they were not being sought by authorities in the UK.
The PSNI are carrying out a major review into the practice in a bid to secure new evidential leads.
So far, nine people who were considered as part of the OTRs scheme have been investigated and all linked inquiries "completed", according to the PSNI.
The force said: "The involvement of OTR nominal(s) in an incident has been examined and there are no opportunities to progress the investigation."
John Downey, from Co Donegal, is known to have mistakenly received a letter of assurance that he was not wanted for arrest.
He used it to escape prosecution for murdering four soldiers in the IRA's Hyde Park bombing of 1982.
That prompted a public outcry and a review of those involved in the scheme.
Crimes linked to 36 OTRs who received official assurances have been assessed and forensic evidence examined as a priority.
The status of those involved had originally been changed from wanted to not wanted.
Suspects not being actively pursued due to a lack of sufficient evidence received a letter from the British government informing them.
Sinn Féin said the concession was necessary to restore confidence in the Briitsh government's commitment to deal with OTRs to ensure the success of arms decommissioning, a 2014 review by senior judge Lady Justice Hallett reported.
The British government has said it was a statement of fact carrying no future guarantees.
Northern Ireland Office (NIO) permanent secretary Sir Jonathan Stephens said: "All the recommendations of Lady Justice Hallett have been implemented with the PSNI continuing their review of the OTR cases giving priority to the 36 individuals, and an additional four individuals identified by the PSNI as priority cases.
"This review, and decisions on further lines of investigation, are operational matters for the PSNI, who regularly update the OTR Oversight Board on general progress."
A DUP spokesman said: "OTRs were a corruption of justice designed by a Labour government in cahoots with Sinn Féin.
"They should never have happened."
