Why do I have to suffer due to a thing that a person in a past life has done that I have no control over?

I am going to be assuming that the "other person" referred was "you" in a previous life. I quoted the "you" as Buddhism asserts there is no self. I somewhat agree with the answer there are no past lives. This is a very hotly contested view in the larger Buddhist community. I personally, have no problem with that view. Stephen Batchelor has spilled a lot of ink in favoring the no past lives view. But let's say you want to keep past lives (probably an ego attachment) then the view of the alaya consciousness asserted by Vasubandhu, an early adherent ti the Yogacara school of Buddhism says (in my understanding) that a deep level consciousness called alaya consciousness is a continuous stream where the alaya consciousness acts as a karmic storehouse. The alaya consciousness may manifest as tendencies in this life. Who knows, maybe genetic correlates of personality. The genetic correlates of personality is hotly debated within the genetics community and it is beginning to look like the interweaving of genetics and the environment may be so complex that trying to tease out a causal model may be too deep(at this point in history). So.... how you choose to look at the nature/nurture question and the alaya consciousness may provide some insight on how you might answer your question. I think the Stephen Batchelor approach is probably more well suited for people deeply enmeshed in Western thinking(linear causality and principle based philosophy, see excellent book "The Uncertain Phoenix" by David Hall ISBN-13: 978-0823210534)

Imagine you were a 10-year-old kid born in a war torn country. The warlord army approached, raped your sisters, killed your brothers and parents, and forced you to become a child soldier who had to shoot and kill people for a living. Needless to say, the level of suffering and pain would be indescribable. Now half a world away, another 10-year-old boy borned into a royal family of a wealthy country who saw this terrible news on TV and gave either one of these 2 responses:

1. Respone1: shrugged his shoulders and said: "Oh well, sh...happens. There's no kamma, things are completely random. By sheer chance the poor kid just happened to be born on the wrong side of the lucky coin of life while I happened to be born on the right side"
2. Response2: things happens for a reason. Although you are not the same person as the guy in a previous life (different body and mind), you are not a completely different one from him either (the kammic stream continues on from one life to the next). Now whether you agree with this truth or not, the fact is you're currently in this terrible situation right now. You've been dealt a terribly lousy hand. But past kamma belongs to the past, what you do right now (your current kamma) is all that matters for it'll have a direct impact on your own life here and now and the many subsequent lives into the future:
   

   "I am the owner of my actions (kamma), heir to my actions, born of my actions, related through my actions, and have my actions as my arbitrator. Whatever I do, for good or for evil, to that will I fall heir". ~~ AN 5.57 ~~

The doctrine of Anatta is so subtle that it simply cannot be understood by mere reasoning or intellectual knowledge.

Only insight meditation practice can lead one to ultimate understanding, i.e. that there exists no being, a man, a woman etc. These are concepts and have no real reference.

Instead there exists a mental and a physical stream which can be understood through the practice of insight meditation.

As Ven. Mahasi Sayadaw says: "In brief, we should understand that life is only a ceaseless causal relationship of mind and matter with consciousness" (Dependent Origination).

Touch, is the cause of suffering, if not-knowing is not touched, if one is not touched, how could suffering arise. Pleasure and pain are caused by touch, Nyom Saptha Visuddhi, and by no other, this, or that man.

And who could solve the problem of still being touched if not one self by listening and putting into practic the path, for the sake of destroying not-knowingness?

[Attention!: This touch of Dhamma is a gift and not meant to get touched with not-knowingness but its destruction, not for using it for commercial purposes or other wordily gains and to keep alive the flames of death and suffering. It has the only purpose to let one come in touch with Dhamma, and it is harmful if using not for the sake of liberation but for the world.]

We can approach it like this:

There are no past lives. There are only the experiences of the individual person's moment, moment by moment.

My past life is my past moment. Your past life is your past moment.

Moments go to the next moment because of change or transcendence.

Birth is a change. Death is a change. Everything is in flux. Birth and death. Rise and fall.

Death of the physical body is simply another moment that seems like a lot of change.

Your friend believes they are suffering due to past life kamma. I have never read such a belief in the Pali suttas. Further, if this belief is true, there is no way for your friend to stop suffering since the causes of the suffering are inaccessible to them since the causes occurred in a past life.

AN 3.61 refutes the (sectarian non-Buddhist) view that suffering arises from past kamma. It states:

When one falls back on what was done in the past as being essential, monks, there is no desire, no effort [at the thought], 'This should be done. This shouldn't be done.' When one can't pin down as a truth or reality what should & shouldn't be done, one dwells bewildered & unprotected.

In Cula-Kammavibhanga Sutta, it is not said suffering (dukkha) arises due to past kamma. It is only said that past kamma determines certain worldly conditions, such as being short-lived, long-lived, sick, healthy, ugly, beautiful, insignificant, influential, poor, rich, low-born (social status), high-born (social status), stupidity & wisdom.

In the teaching of Dependent Origination, which explains how suffering arises, the word 'kamma' does not even exist in the Pali (despite some erroneously translations including the term 'kamma-formations'). Therefore, past kamma is unrelated to Dependent Origination, which explains the ultimate cause of suffering is ignorance.

In the teaching of the Four Noble Truths, it is explained suffering arises due to craving & new becoming occurring in the here-&-now:

And this, monks, is the noble truth of the origination of stress: the craving that makes for new becoming — accompanied by passion & delight, relishing now here & now there — i.e., craving for sensual pleasure, craving to be, craving not to be.

Your friend has the non-Buddhist sectarian view described in AN 3.61. Due to this wrong view, your friend has no solution to suffering & lives unprotected, as is warned in AN 3.61.