A subsidy is a payment to the person.
If a farmer lost money one year, the tax break does not financially benefit him.
Money I have left over from paying taxes is not a "subsidy".
“subsidy is a benefit given to an individual, business, or institution, usually by the government. It can be direct (such as cash payments) or indirect (such as tax breaks). The subsidy is typically given to remove some type of burden, and it is often considered to be in the overall interest of the public, given to promote a social good or an economic policy.” https://www.investopedia.com/terms/s/subsidy.asp
“A subsidy is an incentive given by the government to individuals or businesses in the form of cash, grants, or tax breaks that improve the supply of certain goods and services.” https://corporatefinanceinstitute.com/resources/knowledge/ec...
That’s literally the first two definitions from searching DDG, here’s Wikipedia.
“A subsidy or government incentive is a form of financial aid or support extended to an economic sector (business, or individual) generally with the aim of promoting economic and social policy.[1] Although commonly extended from the government, the term subsidy can relate to any type of support – for example from NGOs or as implicit subsidies. Subsidies come in various forms including: direct (cash grants, interest-free loans) and indirect (tax breaks, insurance, low-interest loans, accelerated depreciation, rent rebates).[2][3] https://en.wikipedia.org/wiki/Subsidy
Often things are written so exactly one company benefits when they agree to build something like a sports stadium in exchange for zero property taxes for N years. If that subsidy isn’t large large enough they may also hand out cash.