Bad as this news is, R/R are in a much better position than during the last recession. They have a much wider range of aircraft carrying their engines for a start, and a much wider customer base, (all those 777's in the US and Asia, a lot of A330's, most 757s).
With the BMW-R/R programmes, and the purchase of Allison, they have the best portfolio of products for a very long time.
R/R customers for the A380 seem to be commited to their delivery, though Virgin may delay.
The A340-500/600 isn't such a pretty picture, but I reckon most ordered will be delivered, it does not matter to R/R if they end up with another airline at a discount, engines still need spares and support.
Plus, the EU200 engine for the Eurofighter is ramping up, as is a range a european helicopters with RTM engines, (EH101, UK Apaches, many of the NH-90s).