Economic theory tells us the price would rise. It would have a deflaitonary effect on bitcoin economy. However because bitcoins are so easily divisible it would not impact the ability for the network to function.
If 90% of bitcoins were lost/destroyed that would leave 2.1 million "whole" bitcoins in circulation. This wouldn't be an issue because currently bitcoin network supports transactions down to one satoshi (0.00000001 BTC) which is 210 trillion discrete units of exchange.
It is possible to allow smaller units of exchange however I will illustrate that is unecessary. The world's money supply (M0) is valued at ~ $20 trillion. If entire world switched to using bitcoin for all commerce the value of a "whole" bitcoin would be $9,524,000 each. However the smallest unit 1 satoshi would be worth $0.10 Even with 90% of bitcoins destroyed/lost there would be sufficient units remaining to allow commerce down to a 10 cent granularity with Bitcoin replacing the entire world's money supply.
It would result in some changes in language. Obviously most people wouldn't value things in terms of bitcoins but rather in smaller units like satoshi's (0.00000001 BTC).
As an example a fastfood meal could be priced as $5USD, 0.00000053 BTC, or 53 satoshi's. Obviously 53 is far easier for humans to express than 0.00000053 BTC despite them having equivelent value. Given the high value of a single BTC, "whole" BTCs would rarely be used other than to express things that are currently express in millions of dollars (like salaries of celebrities, values of corporations, size of national debts, etc).
Satoshi is used as an example but alternatively SI prefixes could be used. For common usage prices in fractional μBTC (micro bitcoins) makes the most sense with 1 μBTC = 1E-6 BTC.
"Man gold broke 200 μBTC today"
"The US Congress raised the minimum wage to 1.50 μBTC effective Jan 1"
"I got the job. Starting salary is 8,400 μBTC a year"