Do people have the same soulmate in their previous lives?

Not necessarily!
One may have the same soulmate as previous life’s in this life – that’s possible. Or one could meet the same person, but in a different relationship – that too is possible. And one may not meet the person at all in future life – that also is very much possible.

When there’s no love, obviously people part ways. And in case it is only one-sided love, then generally, one may meet a different person having similar characteristics, in the next birth. But when the two have intense love for each other, such people could become the life-partners in their next life, and if their love is far more intense, they would have the same soulmate life after life.

The Story of Lord Neminath who had the same soulmate for nine consecutive livesr
In Jain scriptures, there is this famous story of the 22nd Tirthankar Bhagwan Lord Neminath, who shared a loving relationship with Rajul for nine consecutive births. These ideal icons of purity remained fully loyal to each other with their mind, speech and body throughout their life, and they never hesitated to make any kind of sacrifices to support the cause of their soulmate.

In each of their eight previous lives, they remained a soulmate of each other. And in the ninth birth, the two, by the name of Nemikumar and Rajul, were about to make an ideal couple. But just before their marriage, Nemikumar realized that ignorance of one’s real Self leads to wrong perception and consequently wrong actions, the result of which is enormous pain and suffering life after life. Recognizing that it was time for him to take the path that would help him get rid of all his sufferings and lead to happiness of thousands of living beings, he decided to renounce the world.

While Rajul’s family were taken aback by this decision, and in fury were thinking of getting her married to someone else, Rajul in her heart had accepted Nemikumar as her husband. She could not even think of any other person to take his place.
Rajul did not like people cursing Nemikumar. When she came to know the cause of Nemikumar’s renouncement, she endorsed his decision in total agreement of the fact that Nemikumar had left her for a commendable purpose, and hence decided to follow the footsteps of Nemikumar by renouncing the world to attain the ultimate truth.

The love that is true never binds, it is always liberating!
So, if the love for each other is without any selfish desire or expectation, if the love knows only to give to each other, that love will certainly liberate.
When expectations creep in, they adulterate the love, selfishness arises. And when selfishness takes hold in love, that love becomes a bondage which suffocates the other. In that case, they fail to remain a soulmate in their next life.

Therefore, the Enlightened One advises:
To rise in love, practice the following:
Minimize your expectations,
Do not see faults of each other,
Do not hurt each other,
Do not keep any conditions,
Do not say anything negative about that person to someone else. Only say positive things about the person you love to another person. If that happens, do pratikraman (i.e. repent heartily).

Then, the love will elevate to a higher level. If you want to maintain that love, both of you may come to the Enlightened One; you’ll get the right understanding then.

To know more: https://www.dadabhagwan.org/path-to-happiness/relationship/true-love-in-relationship/