Let's step back a little bit from specific teachings on brokenness by Zac Poonen and take a look at what the Bible says.
First, when the Bible talks about brokenness, it talks about repentance.
Let's take a look at Psalm 51 in particular. When David sinned against God and realized his sin, he prayed this prayer.
"For You do not delight in sacrifice, otherwise I would give it;
You are not pleased with burnt offering.
The sacrifices of God are a broken spirit;
A broken and a contrite heart, O God, You will not despise." (Psalm 51:16-17)
Furthermore David said:
"Hide Your face from my sins
And blot out all my iniquities.
Create in me a clean heart, O God,
And renew a steadfast spirit within me." (Psalm 51:9-10)
So brokenness means being saddened and remorseful over one's sin and turning away from that sin.
When you turn away from your sin, you ask God for help at the same time that you put in effort yourself to turn away from that sin.
The Bible tells us to "love the Lord your God with all your heart, and with all your soul, and with all your mind, and with all your strength" (Mark 12:30).
Just like when you take a test, you don't just pray and not study. You pray and study to pass the test. Similarly, with the things of God, you put in your diligence and all your being as well as ask for God's help to succeed. So with 100% God's help and 100% your diligence, you can succeed in overcoming that sin.
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In everything, we need to take a look at what the Bible says and weigh teachings against the Bible. While there may be some biblical teachings from Zac Poonen, there are also some teachings to watch out for.
Brokenness is not having zero emotions when someone criticizes you. It is perfectly ok to feel sad when someone yells at you. The Bible says, "Be angry, and yet do not sin; do not let the sun go down on your anger, and do not give the devil an opportunity." (Ephesians 4:26-27)
Brokenness is also not about repeated failures to overcome strong-will or pride.
Brokenness is being remorseful for one's sin. It is being repentant because a person has sinned. Then the Lord will forgive the person's sin and help him turn away from it.
Please take a look at the following article on the Keswick movement, which Zac Poonen identifies with.
https://www.gotquestions.org/Keswick-movement.html
Sanctification is repentance and working with God to overcome sins and bear fruits of righteousness. It is not about second touch of the Holy Spirit or any particular spiritual experience. But sanctification is a life-long process of practicing righteousness with the help of the Holy Spirit.
Paul said: "Not that I have already obtained it or have already become perfect, but I press on so that I may lay hold of that for which also I was laid hold of by Christ Jesus. Brethren, I do not regard myself as having laid hold of it yet; but one thing I do: forgetting what lies behind and reaching forward to what lies ahead, I press on toward the goal for the prize of the upward call of God in Christ Jesus." (Philippians 3:12-14)
So no one can claim to be perfect even with the baptism of the Holy Spirit. But we press on to continue to practice righteousness and always improve by the power of God.
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When you pray to God regarding something according to His will, God will always give you the best. So when you asked about brokenness, God wants to show you what it truly is according to what His word says. It is important to follow God's word and let that be the test of everything, instead of following a particular person. So please don't be offended if you have followed a particular person for a long time and discover that his teachings are not necessarily biblical.
"Now these were more noble-minded than those in Thessalonica, for they received the word with great eagerness, examining the Scriptures daily to see whether these things were so." (Acts 17:11)
God wants to correct you for the better. God wants to teach you personally when His Spirit convicts you of sin. And He will make you a better person.