I'm not sure what black hose you can be referring to, other than the drain tube. All the other tubes under the cabinet should be part of refrigerant system. I would recommend having a technician come out to check this. It's possible since the water tube or trap was stopped up, the water did find an alternative drain inside the cabinet. In this case, any area of the cabinet seams that appear to have moisture will need to be sealed with some rtv # 482338, which is available at [SearsPartsDirect | partsdirect.com?sid=MMLxexpertxmerch
] . RTV can also be purchased at most any local hardware store. The green residue will probably be mold from the moisture. It will not be freon. If you would like to have a technician check this, you can call 1-800-469-4663 to schedule a tech to come out. Thank you for using Manage My Life.