I assume they did this:
1) Home value increased (greatly)
2) Refinance for a much lower rate (e.g., 3% instead of 6%),
3) Remove the PMI payment cost (which is fairly significant insurance cost)
4) Increased the total amount borrowed, but kept within 80% LTV
5) Increased the number of years remaining on the loan. e.g. they had 22 years remaining on a 30 year loan and bumped it back up to 30 years. (I did not include this in my example below, but it will also lower monthly payment while extending the loan)
So, the monthly payment could now be lower through a combination of longer time to pay off and lower interest and PMI. Even if the loan amount increased. BUT you end up with more payments (years more).
Let's say it was a $200k value home that has increased to $250k in value.
OLD MORTGAGE
Orginal mortgage was 90%, or 180k. 30 year, 6% rate (because they did not have a very long credit history or had a single bad mark). $1079 monthly payment plus PMI (1% assumed) of approx. $150/month = $1229/mo payment
Total to be repaid in remaining 26 years = $295k
Now, 4 years later, their credit history is great. They cleared up the old issue and have more than 2 years of excellent payments plus now a mortgage being paid promptly on their report.
NEW MORTGAGE
New Value x 80% LTV = $200k able to be borrowed, at 3%, 26 yrs.* No PMI.
PMT = $924/mo.
Total to be repaid over 26 years = $288,300
*NOTE -- could increase the payments out to another 30 years and pay even less per month, for more years., and a bit MORE overall to be repaid
In this example, the monthly payment went down by $155/mo and the number of years of payments stayed the same, and the total to be repaid over the life of the loan decreased by $6,700.
They also ended up borrowing an extra $30k (as they had paid off $10k of it, leaving $170k remaining over 4 years and refinanced it at $200k) That $30k went to the new loan origination fees... and they pocketed some, too. Newer car or kitchen upgrade or CC repayments, perhaps.
The main cause of the better numbers was the dramatic drop in interest rates and the removal of PMI. PMI is exceptionally expensive, IMO.