Rail Pass for two travelers not traveling together

Pete, I think the short answer is she won't, unless you risk posting the pass to her.

But, a bigger question is, are you sure buying a pass for Germany is a good idea? If your only trips in Germany are Frankfurt Flughafen to Karlsruhe and Karlsruhe to the Swiss border (Basel), it is almost certainly cheaper to buy normal tickets. For Karlsruhe to Switzerland you can get cheap advance purchase tickets. For Frankfurt Flughafen to Karlsruhe you should not buy in advance as you cannot predict when you will get out of the airport (immigration, late flight ...), but your ticket would I assume be paid for by your work.
Look up times and prices on the German Railways site: https://www.bahn.de/p_en/view/index.shtml

Thanks so much Chris for your expedient and helpful reply! Yes this makes sense to me and yes my employer will pay for the ticket from Frankfurt - Karlsruhe and back. Many thanks!

For Frankfurt Flughafen to Karlsruhe you should not buy in advance as
you cannot predict when you will get out of the airport (immigration,
late flight ...)

In this case I agree, although I don't think this is always the case. Here, the lowest priced, advance purchase ticket for a 1 hour 5 minutes, no change connection by ICE only saves 11 euro vs full fare and risks costing you 17,50€ more than full fare if you can't make the train. There are somewhat less expensive tickets, but they take longer to get to Karlsruhe. In this case, I don't think the savings are worth the extra time.

There is an ICE every hour at 53 past the hour. Odd hours are direct (ex 11:53) and even hours need a change in Mannheim. 40 EUR bought at the airport. Your wife can take the cheap train :)

There are no details here about your journeys within Switzerland. Or are you only traveling to Basel??

It's not uncommon to get a Swiss pass or a rail pass that includes travel in Switzerland because of the high cost of train trips there. Passes often include important discounts for certain private and specialty railways and mountain lifts.

http://www.seat61.com/Swiss-trains.htm#.V96DWzWeaME
http://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#.V96ENzWeaME

Alternatively, there are Swiss (SBB) Supersaver fares within Switzerland - which I've used successfully on separate occasions:
http://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/supersaver-tickets.html

As for getting to Switzerland without a pass, if you and your wife will spend time in Karlsruhe beforehand, I'd consider pre-purchasing a DB saver fare from Karlsruhe to wherever (unless for some reason you just can't pinpoint a travel date and hour.)

Will your wife fly into FRA, then make her own way to Karlsruhe? Or do you plan to meet your wife at FRA airport? And if so, are you heading straight from FRA to Switzerland? In that case, you would still face the issue of flight-delay = forfeiture of a saver fare ticket (although you could minimize the possibility by building in a gap of several hours at FRA airport.)

But if after meeting her at FRA, you are returning to Karlsruhe for a night prior to your trip to Switzerland... the saver fare should work fine. Just book the FRA - Swiss City saver fare using regional trains only for the FRA - Karlsruhe leg on the day she arrives; when you book and use regional trains only for part of a saver pass journey, you can use ANY REGIONAL TRAINS that are convenient for you along the booked route for the date in question. Also, schedule a long stopover for overnight. The site will automatically schedule you for long-distance IC/ICE trains for Karlsruhe - Swiss City the following morning. I just tried this for dummy dates (December 7-8) with a stopover of 21 hours in Karlsruhe at the DB site and came up with a fare of E78/2 adults:
lv. FRA 10/7 9:29 am, ar. Karlsruhe 11:52 am
lv. Karlsruhe 10/8 9:00 am, ar. Bern 11:56 am.

You can try this strategy at the DB query page yourself for the travel dates and for the Swiss destination you have in mind.

With a rail pass: If you plan to meet at FRA, and if you end up wanting a multi-country pass, then it might make sense for you to arrive in Germany with that rail pass in hand for later use on the day your wife arrives - you use the pass on Pass Day #1 to travel solo back to FRA, then as a couple you use the pass again to make tracks for Switzerland (or back to Karlsruhe?)

But only you know what trips you'll be making in Switzerland - and it's that info that should inform your ticket/pass decisions.

Thanks all for your replies! There are so many options! The exact travel is not set in stone yet but it may go something like this. We arrive separately in FRA and travel separately to Karlsruhe. Once we are both in Karlsruhe, we then travel (the next day) together to Switzerland and then most likely travel by rail for a day or two at most entirely inside Switzerland. We then travel from Switzerland directly to FRA. Thanks again!