Question: At this link they show the major holdings for the technology index fund (XLK):  

<http://ca.finance.yahoo.com/q/hl?s=XLK>  

Now let us say the major holding AAPL keeps going down. At what point would the index rearrange itself (either by removing AAPL or decreasing the percentage) so that the overall index stays healthy. I mean....after all, why should just one company drag down a whole index? Also at what point would they consider letting a new company in as part of the index?

Answer: 
An index will drop a company for several reasons: 

* They don't meet the size criteria. Too big or too small
* They don't meet the sector criteria. If Apple dropped all hardware and became a music publisher they wouldn't be a technology company.
* They don't meet the regional requirement. Some indexes are country or region based
* They are no longer listed on the specific exchange. The price of a share may be too low.
* They no longer are an independent company. They merged or were bought.

A fund decides how close they want to mirror the index. Some do so exactly, others only approximate the index.
[S & P Index Announcements](http://www.standardandpoors.com/indices/index-announcements/en/us) would have notes on when there are changes to the index. For example in the S & P Small-cap 600 there is a change that takes affect on Feb. 19, 2013.

As for how index funds handle changes to the fund, this depends a bit on the nature of the fund as open-end mutual funds would be different than exchange-traded funds. [The open-end fund would have to sell and purchase to keep tracking the index which can be interesting to see how well this is handled to keep the transaction costs down](http://en.wikipedia.org/wiki/Index_fund#Index_composition_changes_reduce_return) while [the ETFs will just unload the shares in the redemption units of the stock leaving the index while taking in new shares with creation units of the newly added stock to the index.](http://www.investopedia.com/articles/mutualfund/05/062705.asp)