Tyvek as a shelter is hugely important because of its light weight. Tyvek Home Wrap is very thin (6.4 mil or .064 In), ultra light, at 1.6 Oz. per sq yrd. There are ultralight tents on the market like the Quechua, but they arent as light as Tyvek.
Price is huge when thinking about using Tyvek as shelter. Remember the ultralights that I mentioned earlier? Many of them run in the hundreds of dollars. Tyvek is relatively cheap. For a regular tyvek style shelter at about .11 per square foot (i've found them for this price on ebay) you can have a 10' x 10' tarp for $11.00. Throw in another 10' x 10' ground sheet and now you've got $22.00.
Your Next Step Is..
In the end, instant shelters are very doable. Whether its a pre bought tent or a DIY shelter, you have options. But there is one item that can help you in either situation. Its called a GripClip. You can use these for anything. But when you combine them with Tyvek, garbage bags, tarps or plastic, you get more flexibility. You can find these almost anywhere. WalMart has them.
Another thing to think about is the poles to hold up your tarp. One cool idea is the Kaito BT409 Anti-Shock Hiking Pole with 9-LED Flashlight - $17 on amazon. I’ve been able to find aluminum Walking Poles for $8.00 each. They extend to 54" which is higher than most walking sticks. What that means to you, is your tent will have more room inside for you to sit up wthout banging your head on the sides of your Tyvek tent.