How can I block an outgoing call to a specific number? I have a mentally ill relative who keeps calling a premium-rate telephone number. I want to block her ability to call this specific number because she is able to rack up a very high bill in a matter of hours.

1) Right now she has a feature phone (dumbphone) where as far as I found out it is not possible to block a specific outgoing number, nor do the phone carriers in my country offer the ability to block the calling of premium numbers (or the calling of one specific number).

2) My second option is to buy a cheap smartphone and somehow block this one premium number there. It would be best if I could block the number directly in the phone settings (parental controls or something similar?) and lock the setting with a password. 
Second best option would be to install an app that can again block a specific outgoing number and lock the setting behind a password.

The relative would not be able to root the phone or do anything similarly technical to circumvent the limitation.

3) My third option is to take the phone away from her altogether, but she uses it to stay in contact with other people, so this is a bad solution (albeit one I must reach for in case the other ones fail).

What solution would you recommend to block a specific outgoing phone number? Does some version of Android have parental controls with a block of outgoing calls? Or is there a good app for it?

Thank you.
On Xiaomi phones running MIUI (their Android port) you can restrict calling to a list of fixed dialing numbers or to numbers with certain prefixes. Similar options may be available in other Android phones as well, be sure to check before you buy a phone.

In MIUI 9: 


open the phone app
select menu ('hamburger' icon on bottom left)
select settings
scroll down and select 'Advanced settings'
select 'Fixed Dialing Numbers'


Otherwise, Android apps for parental control should provide that functionality.