This was the historical information about the word they provided:

"Abject" comes from "abjectus," the past participle of the Latin verb "abicere," meaning "to cast off." Its original meaning in English was "cast off" or "rejected," but it is now used to refer more broadly to things in a low state or condition. "Abject" shares with "mean," "ignoble," and "sordid" the sense of being below the normal standards of human decency and dignity. "Abject" may imply degradation, debasement, or servility ("abject poverty"). "Mean" suggests having such repellent characteristics as small-mindedness, ill temper, or cupidity ("mean and petty satire"). "Ignoble" suggests a loss or lack of some essential high quality of mind or spirit ("an ignoble scramble after material possessions"). "Sordid" is stronger than all of these in stressing physical or spiritual degradation and lowness ("a sordid story of murder and revenge").

While abject itself is not used in the NASB a very close synonym is.  The word is wretched.

Paul writes:

Wretched man that I am! Who will set me free from the body of this death? - Romans 7:24

What is Paul speaking about?  Here's some of the surrounding context:

For I know that nothing good dwells in me, that is, in my flesh; for the willing is present in me, but the doing of the good is not.  For the good that I want, I do not do, but I practice the very evil that I do not want.  But if I am doing the very thing I do not want, I am no longer the one doing it, but sin which dwells in me.  I find then the principle that evil is present in me, the one who wants to do good.  For I joyfully concur with the law of God in the inner man, but I see a different law in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin which is in my members.  Wretched man that I am! Who will set me free from the body of this death?  Thanks be to God through Jesus Christ our Lord! So then, on the one hand I myself with my mind am serving the law of God, but on the other, with my flesh the law of sin. - Romans 7:18-7:25

Wretched though we are in our flesh, railing against G-d's Law and authority, our inner man, set free from the "body of death" is able to serve the Law of G-d.  May we all be so... serving G-d according to His commands and living according to His Law.

But wait!  Isn't the Law fulfilled (Romans 8:4)?  Wasn't the Law cancelled  (Col 2:14)?  Did not Messiah come to do the works of the Law so that we do not have to?  Consider Pauls' word from earlier in Romans chapter 7:

So then, the Law is holy, and the commandment is holy and righteous and good. - Romans 7:12

and Paul's word to Timothy:

But we know that the Law is good, if one uses it lawfully, realizing the fact that law is not made for a righteous person, but for those who are lawless and rebellious, for the ungodly and sinners, for the unholy and profane, for those who kill their fathers or mothers, for murderers and immoral men and homosexuals and kidnappers and liars and perjurers, and whatever else is contrary to sound teaching, according to the glorious gospel of the blessed God, with which I have been entrusted.  - 1 Tim 1:8-11

Didn't we start with the passage in which Paul declared himself to be wretched?  If all is complete when we come to faith in Messiah and we are righteous in Him then why does Paul declare himself to be wretched?  Consider also these words of Paul:

For as through the one man's disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous. - Romans 5:19

Paul uses the future tense of the Greek verb.  We cannot be made or declared righteous until there is some trial and a judgment rendered.  Paul tells us that

"...we will all stand before the judgment seat of God."  - Romans 14:10

again in the future tense.  The writer of Hebrews gives us this:

And inasmuch as it is appointed for men to die once and after this comes judgment, so Christ also, having been offered once to bear the sins of many, will appear a second time for salvation without reference to sin, to those who eagerly await Him.  - Hebrews 9:27-28

It seems that the first century understanding of faith, salvation, and justification is that the judgment comes after we die at some future point.  Until then, we remain, like Paul, wretched and abject people.

May we humble ourselves before our G-d and cry out as a tax collector once did:

"God, be merciful to me, the sinner!" - Luke 18:13