DC--> AC Inverter Connected to a single battery in a 6 battery series
Placing a load across only some batteries* in a series string will unbalance the
SOC (state of charge) of the batteries and rapidly lead to damage of some or all of the batteries.   

An exception is if the load is so small compared to the load on the whole battery that the imbalance is able to be rectified by normal charging processes, but this applies only for such small "tapped" loads as to not usually be relevant - see below. 

I'll refer to the batteries in the partial string as the "lower battery" or portion- ie in this case a ground referenced 24 volt portion. The "upper" battery is the 24v string above the lower battery. 

Some battery charging systems provide cell balancing mechanisms that are external to the actual battery operation - but these effectively constitute either
- a charger that selectively charges the lower battery, 
OR 
- a system that discharges the upper battery or prevents it charging further once fully charged in order to avoid overcharging.

Such balance systems are usually intended to accommodate variations in cell performance and are not usually dimensioned to provide substantial current to the lower battery. Systems which do so are available but are usually targeted specifically at applications like this one - for instance in order to operate 12 V equipment from a tap on a 24 V truck or marine system. For practical purposes they can be seen as a charger targeting only the lower battery.

If a battery is severely imbalanced by excess drain from the lower half (or some other portion) then several things can happen.  

On charging


The upper portion will reach full charge first. In "unprotected" batteries the upper portion will then be subject to ongoing current. As such currents are usually well above usual trickle-charge tolerances and as the electrochemical conversion process referred to as "charging" cannot accept more energy, the charge energy is dissipated in some mix of thermal, gas generation or 'electroplating' of electrode components. In the case of Lithium Ion batteries metallic lithium can be plated out and this usually leads to what is euphemistically referred to as "vent with flame". Not quite an explosion but close enough to be exciting. In lead acid cells gassing and electrolyte boiling may occur. NimH and NiCd batteries can dissipate extreme levels of thermal energy and electrolyte is boiled off along the way.
If the battery has protection units per cell or subset of cells  (as LiIon batteries that are required to have unexciting lives all have) the protection units will terminate charging and the lower battery will be less than fully charged. If load continues to be drawn each charge cycle the lower battery will ultimately discharge completely. What happens then varies, as follows ...
Even if the state of imbalance is quite mild the upper battery will attain a higher voltage throughout the charge cycle. If the charging is terminated at the point where the upper battery is correctly charged the lower battery will be less than fully charged. In lead acid battery systems failing to bring the battery to full voltage will cause ongoing damage and shorten lifetime. eg a 12V lead acid battery is "dying" from sulphation of the cells at any time that the terminal voltage is under about 13.7V. LA batteries should be recharged to or above above 13.7 V as soon as possible. An impalanced battery may hold the lower 24V battery under 13.7V x 2 = 27.4V indefinitely and cause progressive accelerated sulphation of the cells. 


On discharging the more discharged lower battery will reach a safe minimum state of charge first. 


Batteries which have low voltage cutout protection per cell or group of cells will terminate discharge. After many cycles you will have an overall battery with the upper half almost fully charged, the lower half almost fully discharged and an effective capacity approaching zero.
Batteries which have no per cell over-discharge protection will drive the cells in the lower battery into undercharge and in extreme cases may completely zero the charge in some cells. If discharge continues the zero SOC cells can be driven first to zero voltage and then into reverse polarity by what is effectively a reverse charging current. Some battery chemistries (notably NiCd and to a lesser extent NimH) can have "whiskers" of metal electroplated across the cell internally. These cause a hard short circuit and resist all usual recharging efforts. While such whiskers can usually be removed by "zapping" with a higher voltage very high current source (large capacitor or eg a car battery !!!), cells which have been whiskered and "restored" are invariably damaged, lose capacity and walk funny for ever after.




8V battery?:

In all cases below except lead acid  N cells &lt;> 8V 
LA can be 8V nominal for cells but this is extremely seldom seen. 
Added 10/2015: I learn something new every day - it happens that, as Chris Thompson says, the Trojan T875is indeed an 8V 4 cell lead acid battery. Trojan ar very competent and capable manufacturers and 'don't make no junk' - no doubt a market niche exists for 8V batteries that I was not aware of. 

Lead acid batteries CAN be nominally 8V but this would be immensely unusual.
Usual LA voltages are 4, 6, 12 and then multiples of 6 or 12V or 2V individual cells.
Lithium Ion is 3.6V nominal, 4.2V max, 3V minimum
LiFePO4 is 3.2V nominal, 3.6V max, 2.8V min
NimH and NiCd are 1.2V min, about 1.3V max, 1V min.
Nickel Iron ? 



*I've used "battery" or "batteries" for "cell" or "cells" where use of "cells" would have been pedantic and/or confused some readers.