There are two verbs spelled "slough" in English, as well as two nouns, and both sets have different pronunciations. The first noun, referring to a swamp or a discouraged state of mind, is pronounced to rhyme with either "blue" or "cow." Its related verb, which can mean "to plod through mud," has the same pronunciation. The second noun, pronounced to rhyme with "cuff," refers to the shed skin of a snake (as well as anything else that has been cast off). Its related verb describes the action of shedding or eliminating something, just like a snake sheds its skin. This "slough" derives from Middle English "slughe" and is distantly related to a Middle High German word meaning "snakeskin."

Hmmm... "cast off".  That sounds familiar:

Jeremiah 31:37

Thus says the LORD, "If the heavens above can be measured And the foundations of the earth searched out below, Then I will also cast off all the offspring of Israel For all that they have done," declares the LORD.

Contrary to the claims of those who subscribe to replacement theology, Isra'el is G-d's people forever.

Many of the references in the Apostolic Writings regarding "cast" don't have to do with sloughing and casting off but rather casting out.

Matthew 8:16

When evening came, they brought to Him many who were demon-possessed; and He cast out the spirits with a word, and healed all who were ill.

The description above about a snake shedding its skin brought this verse to mind:

Acts 9:18-20

And immediately there fell from his [Paul's] eyes something like scales, and he regained his sight, and he got up and was baptized; and he took food and was strengthened. Now for several days he was with the disciples who were at Damascus, and immediately he began to proclaim Jesus in the synagogues, saying, "He is the Son of God."

That particular passage is the only place in Scripture where those "scales" are mentioned.

Messiah spoke the following on the Mount of Olives:

Matthew 24:9-12

Then they will deliver you to tribulation, and will kill you, and you will be hated by all nations because of My name.  At that time many will fall away and will betray one another and hate one another. Many false prophets will arise and will mislead many. Because lawlessness is increased, most people's love will grow cold.

Many will slough off from the body of Messiah?  It seems as though we are in those times.

May we all have the heart and attitude that Paul expressed:

Philippians 3:8-11

More than that, I count all things to be loss in view of the surpassing value of knowing Christ Jesus my Lord, for whom I have suffered the loss of all things, and count them but rubbish so that I may gain Christ,  and may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith, that I may know Him and the power of His resurrection and the fellowship of His sufferings, being conformed to His death;  in order that I may attain to the resurrection from the dead. [emphasis added]

Now to the King eternal, immortal, invisible, the only God, be honor and glory forever and ever. Amen. (1 Tim 1:17)