Derry lie bottom of the league on three points after going down 2-10 to 0-20 to Cork at Celtic Park on Sunday.
Down lost 3-15 to 1-13 to Galway at Newry and are on four points, along with Fermanagh, who were trounced by Meath 3-15 to 0-6 at Navan.
Fermanagh host Derry next Sunday, with Down travelling to take on Cork.
Danny Tallon scored a goal in either half but Derry were unable to contain a dangerous Cork forward line in their Football League encounter.
Cork led 0-10 to 1-6 after a first half which saw play delayed for 15 minutes for treatment to Derry's Jason Rocks.
Tallon's second goal restored parity at 2-9 to 0-15 but points from Colm O'Neill (2) Mark Collins, Paul Kerrigan and Barry O'Driscoll gave Cork victory.
Oak Leafers boss Damian Barton included Slaughtneil pair Chrissy McKaigue and Brendan Rogers in his line-up but it was Cork who moved ahead at 0-4 to 0-2.
Ciaran Mullan replaced the injured Rocks, who was taken away by ambulance, while Cork's Peter Kelleher hit the bar for the visitors.
Tallon found the net late in the half and Benny Heron's point before the break reduced the home side's deficit to one point by the interval.
O'Neill and Neil Forrester traded points at the start of the second half, then Cork pushed ahead, despite Tallon's second goal.
Down went in level with Galway at half-time at Pairc Esler, with Caolan Mooney excelling with two fantastic points from long range.
Darragh O'Hanlon was also a regular points-scorer for the hosts, but the second half began badly for the Ulster county as they conceded two goals within a minute.
Goalkeeper Michael Cunningham was sent-off for a foul on Gary Sice, with Eamonn Brannigan scoring the resulting penalty.
Shane Walsh was next to find the net, although Galway suffered a setback soon after when Declan Kynne received a straight red card for an off-the-ball challenge on Barry O'Hagan.
O'Hagan's goal reduced Down's arrears to 2-9 to 1-9 by 49 minutes but despite three further points by O'Hanlon, it was the visitors who dominated for the remainder of the game.
Marc Reid saved a penalty but Eamonn Brannigan scored on the rebound to help ensure victory for Galway.
Fermanagh got off to a good start with points from Sean Quigley and Ryan Lyons but it was the home side who assumed control thereafter, enjoying a 2-6 to 0-4 advantage by the interval.
Donal Lenihan and Bryan McMahon scored the first-half goals, with Graham Reilly, Bryan Menton, McMahon and Donal Keogan all registering scores.
The Ernemen's other first-half points came from Kane Connor and a Quigley free.
Early second-half points from Sean Tobin and Cillian O'Sullivan were followed by a third Meath goal from Tobin, before Lee Cullen recorded Fermanagh's first score of the second half for 3-9 to 0-5.
Meath scored six of the match's remaining seven points to clinch a comfortable success.
ALLIANZ FOOTBALL LEAGUE RESULTS
Sunday
Division One
Cavan 1-10 0-13 Kerry
Tyrone 0-12 1-10 Mayo
Donegal 1-11 1-11 Monaghan
Division Two
Derry 2-10 0-20 Cork
Meath 3-15 0-6 Fermanagh
Down 1-13 3-15 Galway
Kildare 0-18 1-14 Clare
Division Three
Sligo 2-10 2-14 Offaly
Tipperary 0-12 0-16 Louth
Division Four
Leitrim 2-16 0-15 London
Wexford 0-9 3-24 Westmeath
Wicklow 0-10 1-18 Carlow
Saturday
Division One
Dublin 2-29 0-14 Roscommon
Division Three
Armagh 1-12 0-13 Antrim
Laois 1-13 0-13 Longford
Division Four
Waterford 0-8 0-14 Limerick
Ulster counties Derry, Fermanagh and Down go into next week's final round of fixtures in danger of relegation from Division Two after suffering defeats.