Doesnt seem clear yet how this impacts others. Serie A will be unchanged as Parma got relegated anyway, so the promoted teams from Serie B will stand no matter what. This could happen:
Serie B - One team that was relegated this season will keep their place in Serie B as Parma drop straight through, this will be one of Virtus Entella, Brescia, Cittadella and Varese. All 4 were relegated but I expect one will stay in the division with the other 3 being relegated as they should.
Lega Pro - Four promoted teams will stay as they are to Serie B, these are Novara, Como, Teramo and Salernitana. 9 teams relegated.
Serie D - 9 teams were relegated to Serie D from Lega Pro, as the 9 divisions of Serie D all have different amounts of teams, I would expect the promotions and relegations between Serie D and Lega Pro to remain the same and Parma will go into Serie D/D (due to their location). So in effect 10 teams will drop into Serie D but only 9 will go up.
Scenario 2:
Having said all that, its also likely that the Italian FA would feel that other clubs shouldnt benefit from Parma's poor management by having their relegation reversed. Therefore it wouldnt surprise me if everyones promotions/relegations stand and Parma just get moved from Serie B to Serie D. Meaning that next season Serie B would have 21 teams instead of the 22 it had this season. That would be the most logical approach in my mind and for editing purposes would probably made more sense. Parma will play in Serie D/D though as they are in Emilia-Romagna region of Italy.
Scenario 1 would mean that Serie B has 22 teams again but effectively saves a relegated team. Scenario 2 would be much easier for all concerned.
Also Serie D is the 4th tier of Italian football now after the restructure. Someone said it was 5th tier