Can a takeout doubler pass a redoubled contract?
1D redoubled making 4 is 830 non-vul and 1430 vul according to this (excellent) calculator: http://www.rpbridge.net/xsc1.htm.

Redoubled overtricks count!

Partner should bid 1S. 1S double going down 4 with a probable 4-3 or better fit (LHO or RHO both didn't mention spades) and two Kings seems quite unlikely, and that is against opponents for whom double of 1S will be for penalties. It is probably more useful to play 1S double (by LHO) in this situation for something else (LHO cannot have a trump stack), in which case, you have even more reason to bid 1S.

In this case I would say the problem is with making the takeout double in the first place. (Of course it depends on partnership style and form of scoring, but the below can probably found in most textbooks).

There is a rule of thumb regarding takeout doubles: With a 12-14 hand balanced hand, you should avoid making a takeout double. 

In this case you have a really flat hand, 4-3-3-3, with three cards in the takeout suit. Your hand is defensively oriented with likely 3 defensive tricks in your own hand. 

If you make a takeout double and partner jumps to the three level in your 3 card suit you will likely go down.

Another reason to pass with 12-14 defensive oriented flat hands is that if you have a game, LHO will likely pass and partner will get a chance to reopen.

And to answer the question in the title, sure, a redoubled contract by the takeout doubler can be passed, but it is probably a bad bid.