So trolls are say the axe (which is body spray and not the tool) and layoffs, but lets look at this from a business point of view. A financial company buys a financial company which also has some healthcare companies under it. The new financial company is going to first have to cut with what they know and eliminate redundancy there which is going to be within the finance sector as the look for overlap between products, job roles, workflows, etc. That is the quickest area to cut/layoff.
Within healthcare, it has not been as profitable as other areas, but as a whole has remained profitable. Based on this a evaluation from outside of the new company will most likely be conducted to see if there is a feasible way to increase profitability and what the cost would be to do so. I am guessing that since it was and is the Failure of leadership at DST Systems and DST Health Solutions that cause this imbalance in profits there is a high probability that strategic investments could be made in order to ramp up company potential. Ultimately this would all be done with the intent to split off and sale the health solutions arm. After that sale who know what would happen.
SS&C needs to maintain a good percentage of the people within the Health Solutions side of the company due to their lack of knowledge and experience with healthcare and the most likely outcome of them going to sale the company. For that sale to happen they need new contracts and need to be able to maintain the current contracts and keep the current customers happy. That requires them to keep current DSTHS employees happy and in place to maintain the "status quo" so they can make things look good.
Many layoffs are not likely unless it is at the project level. Projects will most likely be froze and those employees might not be needed. Other layoffs could come in the areas where DSTHS has customers that are not renewing contracts, but keep in mind that these customers are not able to throw a switch and turn everything off there is a long transition period were they are migrated off and phased out so a lot of people will have the opportunity to be absorbed by other teams.