How to find/make a latch that reacts to 0 / 1 inputs and keeps the last state while in high impedance
I'll assume that by  "have the last state of the corresponding output of the TXB0108 preserved" that you mean "... preserved on the non U-controller side of the TXB0108", and that only one line is involved ad that it is always the same line and that it is mono directional and outgoing from the u-controller. And that .. :-).

An adhoc one line unidirectioal "bus-holder" can be made with a non inverting buffer with a resistor from output to input OR
 2 x digital inverters in series (to form a non inverting buffer) with a resistor from output to input.

Using inverters is more common as they are normally more available as part of an overall design - but with hex buffers you'd get twice as many per package. Using Schmitt triggered devices is nicer but not essential. This is essentially a level driven latch.

The first diagram below is simply a non latching inverter.

The second diagram shows a non inverting  buffer with the 3M resistor providing positive feedback for latching. The 1M adds Schmitt trigger action and can be omitted when used as described. The actual value of the '3M' resistor can be  set to suit the situation and logic family. Lower gives a stiffer latch to "pull against". Higher reduces power and makes toggling easier.

The third diagram shows the two inverter version. An advantage is that invered and non inverted latched outputs are available. Again, the 1M adds Schmitt action and is not needed here. The inverters can be Schmitt or non Schmitt types. (CD40106, xx74yyC14, ...)



A bidirectional version can be easily implemented subject to certain limitations. he 1M resistor is omitted and the circuit is driven at its "input". While the drive level exceeds the feedback resistor + inverter drive the input line drive dominates. When the input line goes open circuit / high impebance the lacth self hold via the "3M' resistor and the input line is "latched" by this as well. Making the resistor  lower in value provides more drive. For example, if the drive circuit can easily overcome inverter drive via a 10k resistor then using a 10k provides that level of drive impedance when the input goes to high impedance.

A circuit can be design tailored to an actual need if the need is fully known and ICs to do yur task are probably available as noted by @markrages. 



Above circuits from beam-wiki on Schmitt triggers