If a person is performing ablution (wudu) and he is wearing socks during the ablution, then it is permissible for him to wipe over the socks if he is resident for a period of one day and night. As for a traveler, he can wipe over socks for a period of 3 days and their nights
If he removes his socks, then in this case he cannot wipe over them. The wiping of the socks is broken by three things. First, by removing the socks, secondly, if the time period is exceeded, and thirdly after exposing to the major ritual impurity, such as, post-discharge stage (janaabah) and menstruation that require ritual bath.
If the person is in a state of ablution and he has wiped over his socks, and then the wudu becomes nullified, then in this case if one wants to perform ablution again, one may wipe over the socks. There is no harm in doing so. However, if one removes the socks, then a complete ablution must be made.