Check the exit status of the command. If the command was terminated by a signal the exit code will be 128 + the signal number. From the GNU online documentation for bash:

For the shell’s purposes, a command which exits with a zero exit status has succeeded. A non-zero exit status indicates failure. This seemingly counter-intuitive scheme is used so there is one well-defined way to indicate success and a variety of ways to indicate various failure modes. When a command terminates on a fatal signal whose number is N, Bash uses the value 128+N as the exit status.

POSIX also specifies that the value of a command that terminated by a signal is greater than 128, but does not seem to specify its exact value like GNU does:

The exit status of a command that terminated because it received a signal shall be reported as greater than 128.

For example if you interrupt a command with control-C the exit code will be 130, because SIGINT is signal 2 on Unix systems. So:

while [ 1 ]; do COMMAND; test $? -gt 128 && break; done

It's also possible to use sleep command in while's condition. Making one-liner looking more clean imho.

while sleep 2; do echo thinking; done

while : ; do something ; done &

• Earlier Bourne shells didn't have true and false as built-in commands. true was instead simply aliased to :, and false to something like let 0.

• & at the end of the line backgrounds the process

• : is the null command, as described by "help :": No effect; the command does nothing. Exit Status: Always succeeds.

Not an infinite loop, but a better way to find the actual limit of date:

#!/bin/bash

j=$((1<<61))
i=0
while ((j>0)); do
    if date +'%Y-%m-%d' -d "$((i+j)) days ago" >/dev/null 2>&1; then
    ((i+=j)) ; # printf 'running i %d 0x%x\n' "$i"{,}
    else
    ((j>>=1)); # printf 'new     j %d 0x%x\n' "$j"{,}
    fi
    ((k++))
    # ((k%10)) || printf 'still running %d 0x%x %d %d' "$i"{,} "$j" "$k"
done
printf "final value of limit %d 0x%x in %d loops\n" "$i"{,} "$k"

That will find the limit of date to be:

final value of limit 2147483649 0x80000001 in 64 loops

Remove the comment character # to see how that is done.

It is not a 32 bit number.

That seem to be close to a 32 bit number:

$ printf '%d\n%d\n' "$(( (1<<31) + 1 ))" "0x80000001"
2147483649
2147483649

In fact, is 2**31 + the day number of the month.
If we try with the last day in December (change line 5 in the script above):

date +'%Y-%m-%d' -d "2017-12-31 $((i+j)) days ago"

We get:

final value of limit 2147483679 0x8000001f in 68 loops

That's 31 above 2**31:

$ printf '%d\n%d\n' "$(( (2**31) + 31 ))" "0x8000001f"
2147483679
2147483679

It is also affected by the time zone.

Arithmetic notes

The max value for a shell integer is i less than 2 raised to 63:

$ echo $(( (2**63) - 1 ))
9223372036854775807

We can get the decimal and hexadecimal representation with:

$ printf '%d %x\n' "$(( (2**63) - 1 ))"{,}
9223372036854775807 7fffffffffffffff

That's the maximum number representable in a signed integer of 64 bits (if your system is 64 bits, of course). The next number (just add one) will wrap around (overflow) to a negative number:

$ echo $(( (2**63) ))
-9223372036854775808

$ printf '%d %x\n' "$(( (2**63) ))"{,} 
-9223372036854775808 8000000000000000

Which happens to be the most negative number for signed 64 bit integer.

But a faster way to get the same result is using left shift, which does the same as multiplying a number by two:

$ printf '%d %x\n' "$(( (1<<63) - 1 ))"{,}
9223372036854775807 7fffffffffffffff