This in turns depends on exactly when in the turn the supply phase occurs. For example, if you are in a province that supports 40000 strength points and you send only 30,000 then you are typically okay (assuming no modifiers).
However, if your enemy sends 100,000 strengh points into the province then you are both in trouble if supply is calculated before the battle (assume both toggle to seek battle)
because there will be 140,000 SPs in the province. 
However, if supply is calculated after one army retreats, then if the survivors of your 40,000 hold the field, they are okay
(unless reinforcements came from somewhere else, adding to your forage woes 
).So, Is supply determined after all battles in the province are fought? [&:]