How and why should a Christian be submissive to a corrupted government or selfish employer?

In short:

1. Because it is right.
2. Because it pleases God.
3. Because it answers to a good conscience.
4. Because it gives good testimony to the lost.

I will look at one passage for government and one for employers. First, government:

Romans 13:1Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God.
See All... Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God.  2 Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation.

Paul wrote this during the time of a run of wicked Roman emperors. He died under the hand of Nero. However, even in these circumstances, he advocated obedience to government. The only exception is when government orders a believer to do something against the commandment of God (Acts 4:19-20 [19] But Peter and John answered and said unto them, Whether it be right in the sight of God to hearken unto you more than unto God, judge ye. [20] For we cannot but speak the things which we have seen and heard.
See All...; 5:29
See All...).

Now, as to selfish employers:

1 Peter 2:18-19 [18] Servants, be subject to your masters with all fear; not only to the good and gentle, but also to the froward. [19] For this is thankworthy, if a man for conscience toward God endure grief, suffering wrongfully.
See All... Servants, be subject to your masters with all fear; not only to the good and gentle, but also to the froward. For this is thankworthy, if a man for conscience toward God endure grief, suffering wrongfully.

Servants were to be subject even to those masters who were froward. One who is froward is unruly and contrary. The servant is to submit to him for the sake of conscience and testimony; not because his master was worthy to be obeyed.