For shares purchased through automatic distribution reinvestment, that can be figured out by looking at available (e.g. Yahoo Finance Historical) and seeing what the distribution was ... so if you are missing some records for shares acquired through distribution reinvestment, there is that. I don't know if my ex-tax prep guy uses Yahoo Finance or something else. (He's done that for other clients, he hasn't done that for me because I have the needed information).
Works like for someone who bought 1000 shares of XYZ and just let it sit and accumulate more shares through distribution reinvestment (I use the term "distribution" because for mutual funds, some distributions are capital gains distributions and some are dividends).
Of course it won't tell you what other shares your parents may have been purchased or sold along the way...
Don't know what to tell you, sorry.
You are absolutely right one needs to keep records at least up to 2012 - for mutual funds, I think 2012 is the year when mutual fund companies and brokerages were required to keep track of cost basis.
Yeah it sucks having to keep all the damn statements.
For taxable accounts, I turn off all distribution reinvestments to keep things simple. I take the distributions in cash, and then decide what to do when the cash builds up to a high enough number that it bugs me enough having it earning near-zero return, and then I invest the cash on whatever I want to invest it in (helps with asset allocation rebalancing)
(BTW another advantage of IRAs and 401k's -- none of this applies)
The other thing that some don't realize is FOR EXAMPLE in the simple case of having bought 1,000 shares at $10/share for $10,000, and then doing nothing except let them accumulate shares through distribution reinvestments, until say one has say accumulated an additional 900 shares for a total of 1,900 shares, and let's say the price still happens to be $10/share, so now you have 1,900 shares worth $19,000.
On selling it, one might erroneously and self-harmfully report a capital gain of $9,000: $19,000 (sale proceeds) less $10,000 (the initial purchase price); and pay capital gains tax on a supposed $9,000 of capital gains.
Actually though, there was no capital gain in my example -- all the gain in the number of shares was from the dividends and capital gain distributions being reinvested, for which one paid already paid taxes on every year (dividends and capital gains distributions being reported annually on 1099's). So one should pay $0 capital gains tax. Otherwise are paying double taxes.
(Actually not quite that simple: the share price at which distributions were reinvested has to be considered too in calculating cost basis, so my example and conclusion above is accurate only if the share price had been $10 throughout, so that every share had a cost basis of $10).
All of above is of course just message board rando advice, I claim no expertise, though have talked about this subject a lot with my CPA / tax-preparer and read a lot.
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