It would seem that "total depravity" along with predestination is what defines Calvinism but I submit that all five points of Calvinism go hand in hand. Reformed theology emphasizes the doctrine of grace, best known by the acronym TULIP ,although this really doesn't correspond to the best possible names of the five doctrines.
Since "total depravity" is understood by most I will not take the time to go into great lengths here as you have given the basic meaning which is adequate for the question you have ask. We will need to jump all the way down to the "P" or the "perserverance of the saints" to get into the meat of your question. Actually, a better name for this doctrine would be "the perseverance of God with the saints." God perseveres with and for us, keeping us from falling away, which we would certainly do if He were not with us. Perseverance is the ultimate proof of our election.
The doctrine of perseverance does not rest on our ability to persevere, even if we are regenerated. Rather, it rest on the promises of God to preserve us. Paul writes to the Philippines,
"I am sure of this, He who began a good work in you will bring it to completion at the day of Jesus Christ" (Philippines 1:6)
It is by grace and grace alone that Christian's persevere. God always finishes what He has started. He assures us in His word that His purposes in election are not frustrated.
The golden chain of Romans 8 gives us even further testimony to this hope.
"And those whom he predestined he also called, and those whom he called he also justified, and those he justified he also glorified" (Romans 8:30) Paul goes on to declare that nothing
"Will be able to separate us from the love of God in Christ Jesus our Lord" (8:39)
We have security and assurance because salvation is of the Lord and in His all knowing and craftsmanship He gives the Holy Spirit to every believer as a promise that He will fulfill what He has begun. He has sealed every believer by the Holy Spirit. Yes, He has marked us with an indelible mark and given us His personal down payment that guarantees he will finish the transaction.
A final basis of confidence is found in the high priestly work of our Lord Jesus, who interceded for us, just as He prayed for the restoration of Peter, He also prays for our restoration when we stumble and fall. We may fall for a season but we will never fully or finally fall away. His mighty hand and His promises we find in His Holy word will hold us up. Jesus prayed in the upper room,
while I was with them, I kept them in your name, which you have given me. I have guarded them, and not one of them has been lost except the son of destruction, that the Scripture might be fullfilled." (John 17:12)
Only Judas, who was the son of perdition from the beginning whose profession of faith was spurious was lost. Those who are true believers
cannot be snatched from God's hand (John 10:27-30.
As you can see, although we are a totally depraved people, God gives His chosen a new heart, a regenerated heart, a heart that accepts, cherishes and loves the very things that we were incapable of. He preserves us, He gives us assurance, He holds us up, He will not let His elect or chosen go even tho we are sinners from the very beginning..
5 point Calvints believe in the doctrine of the T-U-L-I-P not because of the belief in Calvin but the absolute truth of Gods word and His promises. His promises are for all that have come to saving faith alone given to us by His grace alone. The assurance that we have is not by OUR perseverance but by His preserving us just as He has promised thru-out the ages. We stand on His promises alone which gives us the confidence, even tho we were depraved from the beginning we are truly His now.
I hope this is a adequate answer to your question. At the heart of Calvinism, we are no different from any other true believer, we accept and believe all that God has revealed to us. We give all the glory and praise to a Sovereign God that deserves all of our worship. He alone is worthy.
Thank you for your time.