Today, I was repairing my soldering iron. During the repair, when I cut the end of two core wire, I found some oil type liquid surrounding both the wire. To confirm, if this is present in whole cable, I cut the wire from other place, and found the same oil type liquid surrounding both the wire there also.
It's probably loss of the plasticizer in the insulation polymer. Flexible plastics like PVC (Polyvinyl Chloride) are not "just" PVC chemically. There are numerous additives to improve fire retardant properties, UV resistance and flexibility. The latter property is improved by the addition of "plasticizer" chemicals, which can make up a significant portion of the material mass. The smell of a swimming pool liner is not the polymer, but the plasticizer. Loss of the plasticizer over time results in gas and/or liquids leaving the plastic and embrittlement of the insulation. Dibutyl phthalate is one example of a plasticizer that is an oily liquid.
Additives of various kinds (in addition to the above-mentioned ones, there are others to improve processing characteristics and to reduce high temperature dechlorination in PVC, for another two examples) have a history of causing problems. High lead levels in homes were found to be a caused by inexpensive (about $10K for a sea-shipment container full, FOB Taiwan) plastic Venetian blinds back in the 1970s. Turns out the manufacturers were using lead as a stabilizer in the plastic and the plastic broke down slowly under UV light (as window blinds are exposed to) and a fine dust containing lead resulted. More recently, some very effective fire-retardant additives have been banned because they are carcinogenic. Other chemicals such as BPA have effects that are disputed, with the EU generally being more eager to ban suspected problem chemicals, and the US EPA being more reluctant to impose costs on business.