John Gregg's Institute have lost eight of their last 10 league games
Institute will finish bottom of the Carling Premiership after they could only manage a draw against Coleraine at Drumahoe on Friday night.
If Donegal Celtic win the Championship, Institute will be relegated but they will go into a two-legged play-off if current leaders DC finish second.
Paddy McLaughlin put Stute ahead on two minutes but Gareth Tommons' 57th-minute goal earned Coleraine a draw.
Stute produced late pressure while Coleraine's Darren Boyce was sent-off.
Boyce received a red card from referee Davy Malcolm after appearing to say something to the match official following a challenge by a Stute player.
Paddy McLaughlin headed Stute into the lead on two minutes after Declan Divin had nodded back a Ryan Semple cross.
Stute were good value for their lead early on as they bossed the opening quarter.
However, Coleraine, despite having little at stake, improved in the second quarter and Boyce, Rory Patterson and their Paddy McLaughlin all missed chances before the break.
Tommons levelled on 57 minutes and Stute needed to regain the lead to keep alive their slim hopes of overhauling second-bottom club Lisburn Distillery.
As Stute produced late pressure, Divin fired wide on 87 minutes while Davy O'Hare saved another Paddy McLaughlin header.
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