Turnbull played for 80 minutes of the game at the Deva Stadium
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Bury have been thrown out of the FA Cup for fielding an ineligible player in their 3-1 second-round replay win over Chester City on 12 December.
Chester have now been reinstated in the competition and will play Ipswich in the third round, as well as receiving the prize due to second-round winners.
Bury can appeal against the decision, and any hearing will take place on Thursday 28 December.
The case relates to Stephen Turnbull, who is a loan signing from Hartlepool.
An FA statement said: "Bury selected Turnbull without receiving the required permission from Hartlepool United and lodging that permission with The FA.
"Bury also failed to comply with the required timescales for registration of players for the FA Cup."