In an area where assessments are automatically re-set at sale prices, the prudent buyer will calculate how much the tax bill will eventually ask for. Elsewhere, it's worth stopping in at the assessor's office and asking for a rough estimate of what the tax is likely to come to, when all the dust has cleared. The buyer of an older home also needs to investigate the tax figure that's quoted in the listing information. It's worth checking whether the present owner has some exemption that makes the tax figure lower than it would be to the next owner. State laws vary, but in some areas senior citizens, or seniors on low incomes may have favorable tax treatment.
Some states offer veterans partial tax exemption.
Tax incentives may be offered to encourage certain agricultural purposes, historic preservation, industry, or other uses. It's even possible to find the present owner being taxed for more than the real tax figure. In some areas, unpaid water bills, for example, might be added to the property tax bill. Again, the matter should be investigated beforehand. Yes, a diligent real estate agent should check with the taxing authorities when the property goes on the market.