Can a fallen angel ask for forgiveness?

What do you man by 'fallen angels' as it is not Scriptural. The Bible does record Jesus saying:

Luke 10:18

New International Version (NIV)

18 He replied, "I saw Satan fall like lightning from heaven.

Revelation 12:4New International Version (NIV)

4 Its tail swept a third of the stars out of the sky and flung them to the earth.

Stars are commonly a reference to angels and a dragon is commonly Satan. These have now been changed by their rebellion and sin into demons which suggest their character is now sealed. The Scripture does not say whether or not they can be forgiven as Jesus died for the sins of mankind. But it says that even after Satan is bound for 1000 years in the pit, he comes out still rebellious and will be thrown into the Lake of Fire for eternal punishment.

Answer:

Absolutely not. Jude 6 tells us: "And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgement of the great day."