I have never examined how bookeeping in Oregon is structured. But I do have experience working as City Manager in another State.
Government Budgets are line item budgets. In other words you would budget almost 12 months ahead of the fiscal year and then go through budget hearings before you would have an approved budget. If Oregon is the same way of budgeting(and I can't say for sure).
The District Attorney may budget similar to this. These numbers are just examples not true numbers:
200,000 for investigators
500,000 cost of trial
400,000 salaries
200,000 operating expenses(rent, bldg upkeep, water, electricity)
75,000 office supplies
200,000 capital purchases like cars, radio equipment etc.
etc. etc. etc.
Now an investigation into a missing child was not anticipated in that budget process and we are probably about 18 months past when the numbers were prepared. Depending on when their fiscal year begins.
So they had this line itemized budget and needed 2 more investigators. There may be unspent money in the line items like operating expenses or office expenses, but it would be against the law to spend that on hiring investigators. My feeling is that they have enough in salaries to pay the person. And they probably got legal permission from the City Attorney to make such a shift. Now if there was another major case then they would have to go back to the well. But, in the line items where they haven't spent the money they will return it because they can't spend it on salaries or investigators.
It is not at all unusual for a Department Head to make a request like the DA made. It puts the City Council on notice that hey we may have an issue , but it also is something tangible. This is a case that needs to be solved and prosecuted. We did this often with Legal Budgets. We budgeted for what we thought we might need but if a big case came in we had to go back and ask for more funding in order to prosecute it or defend against it. City Government has to balance its books. It isn't like the Federal Government that runs in the red.
As I said earlier this comes with a huge disclaimer because I'm not sure how the budget in Oregon is structured but I would imagine it is similar. MOO