(9.49ab) (Proponent of things) “The abandonment that Arhats achieve is not temporary.
They definitely do not take rebirth in samsara again
Because they completely abandon craving, the principal cause of such rebirth.”

The 12 dependent related links explain the mechanism by which samsara perpetuates itself. The short version is if we die with a deluded mind, then it activates contaminated karma which then once again propels us into a samsaric rebirth. The trigger links of the 12 dependent related links are dependent related craving and dependent related grasping. Arhats have completely abandoned all dependent related craving and so therefore they argue there is no trigger to activate contaminated karma to cause another samsaric rebirth. Therefore, they argue, it is not necessary do completely purify all previously accumulated contaminated karma because that which is there never is never activated. This is why the Hinayanists say it is not necessary to realize the emptiness that the Prasangikas explain.

(9.49.cd) But just as you say that they have non-deluded confusion,
Why not also say that they have non-deluded craving?

(9.50) These so-called Arhats have pleasant feelings
That they apprehend to be truly existent.
Because of feeling, craving develops –
So they must be subject to the craving.

(9.51) Although for a person who has not realized emptiness – the lack of truly existent things –
Manifest delusions might be temporarily abandoned, eventually they will manifest again,
Just as feelings and discriminations return when the concentration on the absorption without discrimination ends.
Therefore, you must strive to realize emptiness to attain even solitary liberation.

The main point here is simple:  If you do not root out the root of delusions, the ignorance grasping at an inherently existent self, then delusions will reassert themselves with time, like leaving a trace of roots of weeds.  The danger is very real here, not an academic issue:  It is possible that as a result of practicing Dharma, our mind becomes very peaceful and very happy and we can enjoy many good results.   We can easily become complacent with this.  Worse, we can easily become attached to the pleasant feelings we are experiencing in our mind, and we do not then push further to complete the path.  But if we do not root out the deepest root, such good results will be temporary, and we will eventually find ourselves right back where we are now.  To attain true cessations, we need to realize the emptiness of the mind that is deluded.  This completely eradicates such a mind, and it will never arise again.  Then we attain liberation.

From a technical point of view the reason why the percentages say that individual liberation attained by followers of the proponents of the lower schools is not actual liberation is because the karma too once again be reborn in Sam Sarah remains on their mind. This includes first the tendencies to generate delusions and 2nd the throwing karma to actually take a samsaric rebirth.

It is true if that karma never gets activated the person would never again take sense take a samsaric rebirth. But as long as the tendencies exist on the mind to generate delusions what starts out as non-deluded grasping and non-deluded craving can evolve to become delusions which then once again risk activating throwing karma. The only way to ensure that one never again returns to samsara is to purify all of the tendencies for generating delusions.  If the tendencies to generate delusions no longer exist on the mind then it is impossible for the person to ever generate delusions and then, yes, they would attain actual liberation.  These tendencies to generate delusions are what are known as the delusion obstructions. The other contaminated karma on the mind is known as the obstructions to omniscience. If somebody purifies all of the delusion obstructions, they do not have to purify all the obstructions to omniscience to never again take a samsaric rebirth. However, this other contaminated karma does prevent the attainment of enlightenment and the attainment of the omniscient mind of a Buddha.

The point of this discussion it’s not just to understand the mechanics of samsara but to arrive at the conclusion that the only way to attain even individual liberation is to realize the emptiness that is the lack of true existence. In particular we need to realize the emptiness of the mind that stores all of this karma. At a minimum, it is only by fully and directly realizing emptiness that we can prevent any delusions from arising ever again. When we attain the path of seeing, which is a direct realization of emptiness conjoined with the mind of tranquil abiding, we eliminate all of our intellectually formed delusions. We then continue to meditate on the path of meditation and eventually purify all of our delusion obstructions. We then continue further to meditate on emptiness on the path of meditation with a bodhicitta motivation and then we can purify the obstructions to omniscience and attain enlightenment.